Rewrite as a single logarithm.
-$$\left( \log _ { t } t - \log _ { t } s \right) + 5 \log _ { t } u$$
A) $\log _ { \mathrm { t } } \frac { \mathrm { tu } ^ { 5 } } { \mathrm {~s} }$
B) $\log _ { t } t u ^ { 5 } s$
C) $\log _ { \mathrm { t } } \frac { 5 \mathrm { tu } } { \mathrm { s } }$
D) $\log _ { \mathrm { t } } \frac { \mathrm { t } } { \mathrm { u } ^ { 5 } \mathrm {~s} }$

Question

Quizplus · Accepted Answer

The expression can be simplified using logarithm properties: $\log_a a = 1$, $\log_a \frac{b}{c} = \log_a b - \log_a c$, and $\log_a b^n = n \log_a b$. Applying these, $\log_t t - \log_t s + 5\log_t u = \log_t \frac{t u^5}{s}$.

Rewrite as a Single Logarithm (log⁡tt−log⁡ts)+5log⁡tu\left( \log _ { t } t - \log _ { t } s \right) + 5 \log _ { t } u(logt​t−logt​s)+5logt​u

Rewrite as a Single Logarithm $\left( \log _ { t } t - \log _ { t } s \right) + 5 \log _ { t } u$