Question

solve. round your answer to the nearest thousandth.
$2^{x - 3} = 87$
$x = \square$

Explanation:

Step1: Take log of both sides

Take the logarithm (natural log or common log) of both sides. Let's use natural logarithm ($\ln$). So we have $\ln(2^{x - 3})=\ln(87)$.

Step2: Apply log power rule

Using the power rule of logarithms $\ln(a^b)=b\ln(a)$, we get $(x - 3)\ln(2)=\ln(87)$.

Step3: Solve for x - 3

Divide both sides by $\ln(2)$: $x - 3=\frac{\ln(87)}{\ln(2)}$.

Step4: Calculate the right - hand side

We know that $\ln(87)\approx4.4626$ and $\ln(2)\approx0.6931$. So $\frac{\ln(87)}{\ln(2)}\approx\frac{4.4626}{0.6931}\approx6.4386$.

Step5: Solve for x

Add 3 to both sides: $x = 6.4386+3=9.4386$. Rounding to the nearest thousandth, we get $x\approx9.439$.

Answer:

$9.439$