QUESTION 7 - 1 POINT
Solve: $3^{x+4}=6^{x}$. Enter an exact answer or round your answer to the nearest tenth.
Provide your answer below:
\[
x=
\]
Content attibution
Answer
The solution to the equation $3^{x+4}=6^{x}$, rounded to the nearest tenth, is \(x=\boxed{6.3}\).
Step 1 ：Take the natural logarithm (ln) of both sides of the equation $3^{x+4}=6^{x}$ to simplify it. The properties of logarithms allow us to bring down the exponents.
Step 2 ：Rewrite the equation as $x+4\ln(3)=x\ln(6)$.
Step 3 ：Solve for x to get $x=\frac{4\ln(3)}{\ln(2)}$.
Step 4 ：Calculate the numerical value of this expression to get approximately 6.33985000288462.
Step 5 ：Round this value to the nearest tenth to get 6.3.
Step 6 ：The solution to the equation $3^{x+4}=6^{x}$, rounded to the nearest tenth, is \(x=\boxed{6.3}\).
