Question

Solve the equation. Round to the nearest hundredth. Show work.

$8^{-x+7} = 3^{7x+2}$

Answer 1

Answer:

Final answer is approx x=1.27.

Step-by-step explanation:

Given equation is $8^{-x+7}=3^{7x+2}$.

Now we need to solve equation $8^{-x+7}=3^{7x+2}$ and round to the nearest hundredth.

$8^{-x+7}=3^{7x+2}$

$\log(8^{-x+7})=\log(3^{7x+2})$

$\left(-x+7\right)\cdot\log\left(8\right)=\left(7x+2\right)\cdot\log\left(3\right)$

$-x\cdot\log\left(8\right)+7\cdot\log\left(8\right)=7x\cdot\log\left(3\right)+2\cdot\log\left(3\right)$

$-x\cdot\log\left(8\right)-7x\cdot\log\left(3\right)=2\cdot\log\left(3\right)-7\cdot\log\left(8\right)$

$x\left(-\log\left(8\right)-7\cdot\log\left(3\right)\right)=\left(2\cdot\log\left(3\right)-7\cdot\log\left(8\right)\right)$

$x=\frac{\left(2\cdot\log\left(3\right)-7\cdot\log\left(8\right)\right)}{\left(-\log\left(8\right)-7\cdot\log\left(3\right)\right)}$

Now use calculator to calculate log values, we get:

$x=1.26501646392$

Round to the nearest hundredth.

Hence final answer is approx x=1.27.