Question

Evaluate the logarithm. Round your result to three decimal places.\(\log _{15} 1250\)

Short answer

1.288

Step-by-step solution

Understanding the Logarithm

The logarithmic function presented in the statement: \( \log _{15} 1250 \) represents the following question: to what power must 15 be raised to obtain 1250? This question will guide the following steps

Use the Law of Logarithms

Using the law of logarithms, which states that \( \log_b a = y \leftrightarrow b^y = a \), we can equate 15 to the exponent power equal to 1250. We have \( 15^y = 1250 \)

Solve for y

Solving for the exponent y, involves taking the natural log (ln) of both sides and then manipulating the equation to find y: \( y = \frac{\ln 1250}{\ln 15} \)

Compute the Value of y

Now that we have simplified the expression for y, we substitute the values into the equation and calculate it. After calculating, don't forget to round off your answer to three decimal places.