Question

question
write the expression below as a single logarithm in simplest form.
$3\log_{b}2 - \log_{b}2$

Explanation:

Step1: Combine like logarithmic terms

Both terms are multiples of $\log_b 2$, so subtract the coefficients:
$3\log_b 2 - \log_b 2 = (3-1)\log_b 2$

Step2: Simplify the coefficient

Calculate the difference of the coefficients:
$(3-1)\log_b 2 = 2\log_b 2$

Step3: Apply power rule of logarithms

Use the rule $k\log_b m = \log_b m^k$ to rewrite as a single logarithm:
$2\log_b 2 = \log_b 2^2$

Step4: Simplify the exponent

Compute $2^2$:
$\log_b 2^2 = \log_b 4$

Answer:

$\log_b 4$