Question

question
write the expression below as a single logarithm in simplest form.
$log_{b} 8 + 2log_{b} 2$

Explanation:

Step1: Apply power rule to second term

Power rule: $k\log_b m = \log_b m^k$
$2\log_b 2 = \log_b 2^2 = \log_b 4$

Step2: Combine logs using product rule

Product rule: $\log_b m + \log_b n = \log_b (m \times n)$
$\log_b 8 + \log_b 4 = \log_b (8 \times 4)$

Step3: Simplify the product inside log

Calculate $8 \times 4 = 32$
$\log_b (8 \times 4) = \log_b 32$

Answer:

$\log_b 32$