Question

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

$2.8$ · $13^{4x} +4.8 = 19.3$

Answer 1

Answer:

Final answer is approx x=0.16.

Step-by-step explanation:

Given equation is $2.8\times 13^{4x} +4.8 = 19.3$

Now we need to solve equation $2.8\times 13^{4x} +4.8 = 19.3$ and round to the nearest hundredth.

$2.8\times 13^{4x} +4.8 = 19.3$

$2.8\times 13^{4x} = 19.3-4.8$

$2.8\times 13^{4x} = 14.5$

$13^{4x} = \frac{14.5}{2.8}$

$13^{4x} = 5.17857142857$

$\log(13^{4x}) = \log(5.17857142857)$

$4x \log(13) = \log(5.17857142857)$

$4x = \frac{\log(5.17857142857)}{\log\left(13\right)}$

$4x = 0.641154659628$

$x = \frac{0.641154659628}{4}$

$x = 0.160288664907$

Round to the nearest hundredth.

Hence final answer is approx x=0.16.