If 2^(x) = 1/32 , find the value of x

Question

If
`2^(x)` = 1/32 , find the value of x

Answer 1

Explanation:

you have to make sure the bases are the same

2 multiplied by itself 5 times equals 32

then equate the powers and solve for x

Answer 2

x = -5

Explanation:

Given the equation of:

`\displaystyle{2^x = (1)/(32)}`

32 can be written in an exponential form of base 2 as 2⁵ since 2⁵ equals to 32.

`\displaystyle{2^x = (1)/(2^5)}`

Apply the law of exponent where:

`\displaystyle{(1)/(a^n) = a^(-n)}`

Therefore:

`\displaystyle{2^x = 2^(-5)}`

We have same base for both sides. Compare and consider the exponents only:

`\displaystyle{x=-5}`

Therefore, the value of x is -5.