Set up an equation and apply the definition of a logarithm.
4
Practice makes perfect
To evaluate the given logarithm, we will start by writing a logarithmic equation.
log_4 256=x
In order to solve this equation, we can rewrite it as an exponential equation by using the definition of a logarithm.
log_b x=y ⇔ x= b^y
The above means that the logarithm y is the exponent to which b must be raised to get x. For our exercise, y is the exponent to which 4 must be raised to get 256.
log_4 256=x ⇔ 256= 4^x
Finally, to solve the exponential equation, we will rewrite the terms so that they have a common base.
