Question
If
where
determine b –
- 25
- 5
- 625
- 16
Hint:
logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if
, in which case one writes x =
.
The correct answer is: 5
If
where
determine b –
![log subscript c space 2 times log subscript b space 625 equals log subscript 10 space 16 times log subscript c space 10
fraction numerator log subscript b space 2 over denominator log subscript b space c end fraction times log subscript b space 625 equals log subscript 10 16 times fraction numerator log subscript b space 10 over denominator log subscript b space c end fraction
log subscript b space 2 times log subscript b space 625 equals log subscript 10 16 times log subscript b space 10
fraction numerator log subscript b space 2 over denominator log subscript b space 10 end fraction times log subscript b space 625 equals log subscript 10 16 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left curly bracket space space W e space k n o w space t h a t space semicolon space log subscript b a equals fraction numerator log subscript d a over denominator log subscript d b end fraction space right curly bracket
log subscript 10 2 times log subscript b space 625 equals log subscript 10 16 space space space space space space space space space space space space space space space space
log subscript b space 625 equals fraction numerator log subscript 10 16 over denominator log subscript 10 2 end fraction
log subscript b space 625 equals log subscript 2 16
log subscript b space 625 equals log subscript 2 2 to the power of 4
log subscript b space 625 equals 4
o r comma space b to the power of 4 equals 625 space
o r comma space b equals 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Just like we can change the base b for the exponential function, we can also change the base b
for the logarithmic function. The logarithm with base b
is defined so that
Related Questions to study
Statement 1:The two Fe atoms in
have different oxidation numbers
Statement 2:
ions decolourise
solution
Statement 1:The two Fe atoms in
have different oxidation numbers
Statement 2:
ions decolourise
solution
, where
and
is
In this question, we have to find the . Here Solve first B. In B, rationalize it means multiply it denominator by sign change in both numerator and denominator
, where
and
is
In this question, we have to find the . Here Solve first B. In B, rationalize it means multiply it denominator by sign change in both numerator and denominator
Statement 1:The equivalence point refers the condition where equivalents of one species react with same number of equivalent of other species.
Statement 2:The end point of titration is exactly equal to equivalence point
Statement 1:The equivalence point refers the condition where equivalents of one species react with same number of equivalent of other species.
Statement 2:The end point of titration is exactly equal to equivalence point
If and
are the roots of the equation
then the value of
equals
If and
are the roots of the equation
then the value of
equals
Statement 1:Iodimetric titration are redox titrations.
Statement 2:The iodine solution acts as an oxidant to reduce the reductant
Statement 1:Iodimetric titration are redox titrations.
Statement 2:The iodine solution acts as an oxidant to reduce the reductant
Statement 1:Diisopropyl ketone on reaction with isopropyl magnesium bromide followed by hydrolysis gives alcohol
Statement 2:Grignard reagent acts as a reducing agent
Statement 1:Diisopropyl ketone on reaction with isopropyl magnesium bromide followed by hydrolysis gives alcohol
Statement 2:Grignard reagent acts as a reducing agent
The first noble gas compound obtained was:
The first noble gas compound obtained was:
Given that and
then value of
equals –
These four basic properties all follow directly from the fact that logs are exponents.
logb(xy) = logbx + logby.
logb(x/y) = logbx - logby.
logb(xn) = n logbx.
logbx = logax / logab.
Given that and
then value of
equals –
These four basic properties all follow directly from the fact that logs are exponents.
logb(xy) = logbx + logby.
logb(x/y) = logbx - logby.
logb(xn) = n logbx.
logbx = logax / logab.
Statement 1:Change in colour of acidic solution of potassium dichromate by breath is used to test drunk drivers.
Statement 2:Change in colour is due to the complexation of alcohol with potassium dichromate.
Statement 1:Change in colour of acidic solution of potassium dichromate by breath is used to test drunk drivers.
Statement 2:Change in colour is due to the complexation of alcohol with potassium dichromate.
Total number of solutions of sin{x} = cos{x}, where {.} denotes the fractional part, in [0, 2] is equal to
In this question, we have to find the number of solutions. Here we have fractional part of x. It is {x} and {x}= x-[x]. The {x} is always belongs to 0 to 1.
Total number of solutions of sin{x} = cos{x}, where {.} denotes the fractional part, in [0, 2] is equal to
In this question, we have to find the number of solutions. Here we have fractional part of x. It is {x} and {x}= x-[x]. The {x} is always belongs to 0 to 1.
Statement 1:If a strong acid is added to a solution of potassium chromate it changes itscolour from yellow to orange.
Statement 2:The colour change is due to the oxidation of potassium chromate.
Statement 1:If a strong acid is added to a solution of potassium chromate it changes itscolour from yellow to orange.
Statement 2:The colour change is due to the oxidation of potassium chromate.
Total number of solutions of the equation 3x + 2 tan x = in x
[0, 2
] is equal to
In this question, we use the graph of tanx . The intersection is the total number of solutions of this equation. The graph region is [ 0, 2π ].
Total number of solutions of the equation 3x + 2 tan x = in x
[0, 2
] is equal to
In this question, we use the graph of tanx . The intersection is the total number of solutions of this equation. The graph region is [ 0, 2π ].
The number of sigma bonds in
is:
The number of sigma bonds in
is:
Statement 1:Oxidation number of Ni in is zero.
Statement 2:Nickel is bonded to neutral ligand carbonyl.
Statement 1:Oxidation number of Ni in is zero.
Statement 2:Nickel is bonded to neutral ligand carbonyl.
Suppose equation is f(x) – g(x) = 0 of f(x) = g(x) = y say, then draw the graphs of y = f(x) and y = g(x). If graph of y = f(x) and y = g(x) cuts at one, two, three, ...., no points, then number of solutions are one, two, three, ...., zero respectively.
The number of solutions of sin x = is
In this question, we have drawn the graph. The number of intersections of both function fx and gx are the number solutions. Draw the graph carefully and find the intersection points.
Suppose equation is f(x) – g(x) = 0 of f(x) = g(x) = y say, then draw the graphs of y = f(x) and y = g(x). If graph of y = f(x) and y = g(x) cuts at one, two, three, ...., no points, then number of solutions are one, two, three, ...., zero respectively.
The number of solutions of sin x = is
In this question, we have drawn the graph. The number of intersections of both function fx and gx are the number solutions. Draw the graph carefully and find the intersection points.