Question

im glad youre feeling more confident. how would you complete the problem 16 = 2(3^x)?

Explanation:

Step1: Isolate the exponential term

Divide both sides by 2.
$16\div2 = 2(3^{x})\div2$
$8 = 3^{x}$

Step2: Take the natural - logarithm of both sides

$\ln(8)=\ln(3^{x})$

Step3: Use the logarithm property $\ln(a^{b})=b\ln(a)$

$\ln(8)=x\ln(3)$

Step4: Solve for $x$

$x = \frac{\ln(8)}{\ln(3)}$
Since $\ln(8)=\ln(2^{3}) = 3\ln(2)$, then $x=\frac{3\ln(2)}{\ln(3)}$. Using a calculator, $\ln(2)\approx0.693$ and $\ln(3)\approx1.099$, so $x=\frac{3\times0.693}{1.099}=\frac{2.079}{1.099}\approx1.89$.

Answer:

$x=\frac{\ln(8)}{\ln(3)}\approx1.89$