What is the value of log5(5^9)?

To determine the value of log5(5^9), we can utilize a fundamental property of logarithms. The logarithm of a number to its own base simplifies the expression significantly.

In this case, we are looking for the logarithm of 5 raised to the power of 9 with the base of 5. According to the property of logarithms:

log_b(b^x) = x,

where b is the base and x is the exponent. This means that the logarithm of a number base raised to an exponent simply equals the exponent itself when the base of the logarithm matches the base of the exponent.

Applying this property here, we have:

log5(5^9) = 9.

This confirms that the value of log5(5^9) is indeed 9. Understanding this logarithmic property is crucial as it simplifies many calculations involving exponents and logarithms.