Given the exponential equation 2^x = 128, what is the logarithmic form of the equation in base 10?

Solution:

Logs (or) logarithms are nothing but another way of expressing exponents.

Given:

Exponential equation 2^x = 128

We need to convert the above equation in logarithmic form,

First apply log both sides with base 10

log₁₀2^x = log₁₀128

We know, log a^m = m log a

x log₁₀2 = log₁₀128

Now, divide by log₁₀2 both sides

x = log₁₀128 / log₁₀2

Therefore, the logarithmic form of the equation in base 10 is x = log₁₀128 / log₁₀2.

Given the exponential equation 2^x = 128, what is the logarithmic form of the equation in base 10?

Summary:

Given the exponential equation 2^x = 128, the logarithmic form of the equation in base 10 is x = log₁₀128 / log₁₀2.