Question

solve the equation. log _4 5+log _4 x = 0 select the correct choice below and fill in any answer boxes. oa. x = (simplify your answer, including any radicals. use in ob. there is no solution.

Explanation:

Step1: Use log - addition rule

According to the rule $\log_a M+\log_a N = \log_a(MN)$, we can rewrite the left - hand side of the equation $\log_4 5+\log_4 x$ as $\log_4(5x)$. So the equation becomes $\log_4(5x)=0$.

Step2: Convert from logarithmic to exponential form

The logarithmic equation $\log_a b = c$ can be rewritten in exponential form as $a^c = b$. For the equation $\log_4(5x)=0$, we have $4^0 = 5x$.

Step3: Solve for x

Since $4^0=1$, the equation $4^0 = 5x$ simplifies to $1 = 5x$. Then, dividing both sides by 5, we get $x=\frac{1}{5}$.

Answer:

A. $x=\frac{1}{5}$