Question

solve for $x$, rounding to the nearest hundredth.
$85 \cdot 3^{x} = 765$

Explanation:

Step1: Isolate the exponential term

Divide both sides by 85:
$\frac{85 \cdot 3^x}{85} = \frac{765}{85}$
$3^x = 9$

Step2: Convert to logarithmic form

Take log base 3 of both sides:
$x = \log_3 9$
Or use change of base formula:
$x = \frac{\ln 9}{\ln 3}$

Step3: Calculate and round

Simplify or compute the value:
$\frac{\ln 9}{\ln 3} = \frac{2\ln 3}{\ln 3} = 2$
(Alternatively, calculating numerically gives the exact value 2.00)

Answer:

$2.00$