Given the exponential equation 2^x = 8, what is the logarithmic form of the equation in base 10?

Solution:

It is given that,

Exponential equation 2^x = 8.

We have to find the logarithmic form of the equation in base 10.

By the change base rule (inverse of exponential function)

a^b = c is equal to log_a(c) = b

So, 2^x = 8 in to logarithm from log₂(8) = x

Then into the base 10 logarithmic form.

By the change of base formula

log_b(a) = log₁₀(a)/log₁₀(b)

Then, log₂(8) = log₁₀(8)/log₁₀(2)

Therefore, the logarithmic form of the equation in base 10 is log₁₀(8)/log₁₀(2)

Given the exponential equation 2^x = 8, what is the logarithmic form of the equation in base 10?

Summary:

Given the exponential equation 2^x = 8, the logarithmic form of the equation in base 10 is log₁₀(8)/log₁₀(2).