Maths-
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Easy

Question

If log subscript c space 2 times log subscript b space 625 equals log subscript 10 space 16 times log subscript c space 10 where c greater than 0 semicolon c not equal to 1 semicolon b greater than 1 semicolon b not equal to 1 determine b –

  1. 25
  2. 5
  3. 625
  4. 16

hintHint:

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 b to the power of x space end exponent equals space n, in which case one writes x = log subscript b n.

The correct answer is: 5


    If log subscript c space 2 times log subscript b space 625 equals log subscript 10 space 16 times log subscript c space 10 where c greater than 0 semicolon c not equal to 1 semicolon b greater than 1 semicolon b not equal to 1 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 5

    Just like we can change the base bb for the exponential function, we can also change the base bb for the logarithmic function. The logarithm with base bb is defined so that log subscript b subscript blank end subscript c space equals space k

     

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