14) Solve for $x : 5^{x} = 3^{x + 1}$
a) $\frac{\log 3}{\log 5}$
b) $◯$
$\frac{\log 5 - \log 3}{\log 3}$
c) 0
$\frac{\log 3}{\log 5 - \log 3}$
d) 0
$\frac{\log 3}{\log 5 + \log 3}$

Answer

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Answer

$x \approx 2.15$ is the final answer.

Steps

Step 1 ：Given the equation $5^{x} = 3^{x + 1}$ , we can take the logarithm of both sides to get $x \log 5 = (x + 1) \log 3$ .

Step 2 ：Rearrange the equation to $x \log 5 - x \log 3 = \log 3$ .

Step 3 ：Factor out $x$ on the left side of the equation to get $x (\log 5 - \log 3) = \log 3$ .

Step 4 ：Solve for $x$ by dividing both sides of the equation by $(\log 5 - \log 3)$ to get $x = \frac{\log 3}{\log 5 - \log 3}$ .

Step 5 ：However, the actual solution is approximately $x \approx 2.15$ , which is not listed in the given options.

Step 6 ： $x \approx 2.15$ is the final answer.