Question

Given the exponential equation 4x = 64, what is the logarithmic form of the equation in base 10?

x = log base 2 of 64, all over log base 2 of 4
x = log base 2 of 4, all over log base 2 of 64
x = log base 10 of 64, all over log base 10 of 4
x = log base 10 of 4, all over log base 10 of 64

Answer 1

$4^{x} = 64$

By taking logarithmic of base 10

∴ $log 4^{x} = log 64$

∴ x log 4 = log 64

∴ $x = \frac{log \ 64}{log \ 4}$
note: we don't need to write the base in case of the base =10

∴ The correct choice is
x = log base 10 of 64, all over log base 10 of 4

Answer 2

The correct answer is
 x = log base 10 of 64, all over log base 10 of 4