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_()15 625=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 15 must be raised to get 625.
log_(15) 625=x ⇔ 625=( 1/5)^x
Finally, to solve the exponential equation, we will rewrite the terms so that they have a common base.
Now we have two equivalent expressions with the same base. If both sides of the equation are equal, the exponents must also be equal.
( 15)^(- 4)=( 15)^x ⇔ x=- 4
