Find x for the following equation.
$$
7^{9 x+7}=2
$$
$$
\mathrm{x}=\square
$$
(Do not round until the final answer. Then round to three decimal places as needed. Use a comma to separate answers as needed.)

Question

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To solve the equation $7^{9x + 7} = 2$, we take the logarithm of both sides. ‖ ‖ step 2 ⋮ This gives us $9x + 7 = \log_7(2)$. ‖ ‖ step 3 ⋮ Rearranging the equation, we find $9x = \log_7(2) - 7$. ‖ ‖ step 4 ⋮ Dividing by 9, we get $x = \frac{\log_7(2) - 7}{9}$. ‖ ‖ step 5 ⋮ Using the change of base formula, we can express $\log_7(2)$ as $\frac{\log(2)}{\log(7)}$. Thus, $x = \frac{\frac{\log(2)}{\log(7)} - 7}{9}$. ‖ ‖ step 6 ⋮ Finally, we can simplify this to $x = \frac{2i\pi n - 7\log(7) + \log(2)}{9\log(7)}$ where $n \in \mathbb{Z}$. ‖ ∻Answer∻ ⚹ $x = \frac{\log(2) - 7\log(7)}{9\log(7)}$ ⚹ ∻Key Concept∻ ⚹ Solving exponential equations using logarithms ⚹ ∻Explanation∻ ⚹ The solution involves taking the logarithm of both sides to isolate the variable in the exponent. This allows us to express the solution in terms of logarithmic functions. ⚹◊What steps can you follow to isolate $ x $ in the equation $ 7^{9x+7} = 2 $?⍭ Generate me a similar question◊

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