Maths-

General

Easy

Question

# Solve for the value of m of the following-

a. 7^{m} = 343

b. 2^{m-3} = 1

Hint:

### In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as an, where a is called the base and n is its power/ exponent.

an = a × a × ... × a n times.

## The correct answer is: For both the given equations, m = 3.

### Step-by-step solution:-

a. 7^{m} = 343

∴ 7^{m} = 7^{3}

∴ m = 3 …............................. (Exponents of the same base in an equation are equal)

b. 2^{m-3} = 1

We know that b^{0} = 1 i.e. Anything raised to 0 is equal to 1.

Since we have 1 in the RHS of the given equation, we can conclude that-

2^{m-3} = 2^{0} ................ (because 2^{0} = 1)

∴ m-3 = 0 ................. (Exponents of the same base in an equation are equal)

∴ m = 3

Final Answer:-

∴ For both the given equations, m = 3.

### Related Questions to study

Maths-

### of an isosceles triangle ABC is acute in which AB = AC and BDAC . Prove that

### of an isosceles triangle ABC is acute in which AB = AC and BDAC . Prove that

Maths-General

Maths-

### Convert the following fraction to decimal

a) 9/11

### Convert the following fraction to decimal

a) 9/11

Maths-General

Maths-

### Express the following recurring decimals as vulgar fraction

b) 0.743434343......

### Express the following recurring decimals as vulgar fraction

b) 0.743434343......

Maths-General

Maths-

### ABC is a triangle in which AB = AC. P is any point in its interior such

that. Prove that AP bisects

### ABC is a triangle in which AB = AC. P is any point in its interior such

that. Prove that AP bisects

Maths-General

Maths-

### Evaluate:

a^{−3}b^{−4} / a^{−2}b^{−3}

### Evaluate:

a^{−3}b^{−4} / a^{−2}b^{−3}

Maths-General

Maths-

### Prove that ∠BAC ≅ ∠CAD

### Prove that ∠BAC ≅ ∠CAD

Maths-General

Maths-

### Express the following recurring decimals as vulgar fraction

a) 0.444444444

### Express the following recurring decimals as vulgar fraction

a) 0.444444444

Maths-General

Maths-

### (3^{2})^{3} + (2/3)^{0} + 3^{5} × (1/3)^{4}

### (3^{2})^{3} + (2/3)^{0} + 3^{5} × (1/3)^{4}

Maths-General

Maths-

### Express 0.5248 in the lowest form.

### Express 0.5248 in the lowest form.

Maths-General

Maths-

### Write the following numbers in the scientific notation : 0.00000000065

### Write the following numbers in the scientific notation : 0.00000000065

Maths-General

Maths-

### Write the following numbers in the scientific notation : a) 5,07,460000000

### Write the following numbers in the scientific notation : a) 5,07,460000000

Maths-General

Maths-

### A town has about 25,00 people living in it and the mayor wants to send each person 10,00 as a celebration gift because the town won the Federal Lottery for Small Towns. How much money would the town need to give out this celebration gift?

### A town has about 25,00 people living in it and the mayor wants to send each person 10,00 as a celebration gift because the town won the Federal Lottery for Small Towns. How much money would the town need to give out this celebration gift?

Maths-General

Maths-

### The temperature halfway to the Sun from venus is approximately 1,800° c and scientists theorize that it may be up to 26,000 times hotter at the center of the Sun. Approximately how hot is it at the center of the Sun?

### The temperature halfway to the Sun from venus is approximately 1,800° c and scientists theorize that it may be up to 26,000 times hotter at the center of the Sun. Approximately how hot is it at the center of the Sun?

Maths-General

Maths-

### A state has an area of approximately 9,604,100,000 square miles and has approximately 110,000 people. How much area is this per person?

### A state has an area of approximately 9,604,100,000 square miles and has approximately 110,000 people. How much area is this per person?

Maths-General

Maths-

### Convert the following fractions to repeating decimals

d)

### Convert the following fractions to repeating decimals

d)

Maths-General