Question

Explain how to find the value of ${\log }_{7}15$ using your calculator.

Short answer

The value of ${\log }_{7}15$ by using the calculator is $1.392$

Step-by-step solution

Step 1. Given

An expression${\log }_{7}15$

To find the value of ${\log }_{7}15$

Step 2. Use the Change-of-Base Formula.

Use the Change-of-Base Formula.

${\log }_{a}M=\frac{{\log }_{b}M}{{\log }_{b}a}$

Step 2. Identify a and M.

Identify $a$and $M$. Choose $10$for $b$

${\log }_{7}15=\frac{{\log }_{10}15}{{\log }_{10}7}$

Step 4. Enter the expression into the calculator.

Enter the expression in the calculator using the log button for base $10$. Round to three decimal places.

$\frac{{\log }_{10}15}{{\log }_{10}7}\approx 1.392$