Write in logarithmic form:

Left-hand side: .

Right-hand side: .

Step-by-step explanation:

Apply the logarithm power rule: for all .

This property is not only true for logarithm to the base , but for other bases, as well.

Take the logarithm (to the base ) of the left-hand side of this equation:

.

For the right-hand side of this equation, consider the logarithm quotient rule:

for all and .

Indeed, on the right-hand side of this equation, and . Therefore:

.

This expression could be further simplified. Notice that is equivalent to for all . (Think about how whereas .)

Therefore, would be equivalent to . Apply the logarithm power rule to show that .

.

Indeed, the left-hand side of this equation matches the right-hand side.

answer: true

step-by-step explanation: