Question

question
write the expression below as a single logarithm in simplest form.
$2\log_{b} 7$

Explanation:

Step1: Recall the power rule of logarithms

The power rule of logarithms states that \( n\log_b a=\log_b a^n \), where \( n \) is a real number, \( a>0 \), and \( b>0, b
eq1 \).

Step2: Apply the power rule to the given expression

In the expression \( 2\log_b 7 \), we have \( n = 2 \), \( a=7 \), and base \( b \). Using the power rule \( n\log_b a=\log_b a^n \), we substitute the values:
\( 2\log_b 7=\log_b 7^2 \)

Step3: Simplify the exponent

Calculate \( 7^2 = 49 \). So the expression becomes \( \log_b 49 \)

Answer:

\( \log_b 49 \)