Solve $4^{x+2}=5^{x}$. Enter an exact answer or round your answer to the nearest tenth. Do not include " $x=$ " in your answer.

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Answer

Round the solution to the nearest tenth to get $\boxed{12.4}$

Steps

Step 1 ：Given the equation $4^{x+2}=5^{x}$

Step 2 ：Take the logarithm of both sides to get $\log(4^{x+2}) = \log(5^{x})$

Step 3 ：Use the properties of logarithms to bring down the exponents, resulting in $(x+2)\log(4) = x\log(5)$

Step 4 ：Isolate x to find the solution, which gives $x = -\log\left(\frac{2^{4}}{\log\left(\frac{4}{5}\right)}\right)$

Step 5 ：Evaluate this expression numerically to get an approximate solution of 12.4251348780216

Step 6 ：Round the solution to the nearest tenth to get $\boxed{12.4}$