Write the following as a single logarithm. Assume all variables are positive. $$ \log _{4}(6)+7 \log _{4}(x)= $$ The answer format in lowercase characters is: log_base (number) Spaces in the answer are optional.

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UpStudy AI · Accepted Answer

We start with
$$
\log_4(6) + 7 \log_4(x).
$$
Using the power rule of logarithms, we rewrite $$7 \log_4(x)$$ as
$$
\log_4(x^7).
$$
Now, we combine the two logarithms using the product rule:
$$
\log_4(6) + \log_4(x^7) = \log_4(6x^7).
$$

Thus, the final answer is:

$$
\text{log}_4(6x^7)
$$
log₄(6x⁷)

Write the following as a single logarithm. Assume all variables are positive. \( \log _{4}(6)+7 \log _{4}(x)= \) The answer format in lowercase characters is: log_base (number) Spaces in the answer are optional.

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