Question

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simplify. enter the result as a single logarithm with a coefficient of 1.
to enter the log, click in the answer cell, then click on the small yellow arrow on the right.
then click the functions tab to access the log. if needed, you can change the base.
using the keyboard, you can also enter $\log _{3}(5 x^{4})$ as $\log _{-} 3(5 x^{\wedge} 4)$.
$\log _{7}(4 x^{8})+\log _{7}(11 x^{5})$

Explanation:

Step1: Use the logarithm addition rule

The rule is \(\log_{a}(M)+\log_{a}(N)=\log_{a}(M\times N)\).
So, \(\log_{7}(4x^{8})+\log_{7}(11x^{5})=\log_{7}(4x^{8}\times11x^{5})\).

Step2: Simplify the product inside the log

When multiplying \(4x^{8}\times11x^{5}\), use the rule \(a^{m}\times a^{n}=a^{m + n}\) for exponents and \(4\times11 = 44\).
\(4x^{8}\times11x^{5}=44x^{8 + 5}=44x^{13}\).

Answer:

\(\log_{7}(44x^{13})\)