Solve the equation. Round to the nearest hundredth. Show work.[tex]2.8[/tex] · [tex]13^{4x} +4.8 = 19.3[/tex]

Answer:Final answer is approx x=0.16.Step-by-step explanation:Given equation is [tex]2.8\times 13^{4x} +4.8 = 19.3[/tex]Now we need to solve equation [tex]2.8\times 13^{4x} +4.8 = 19.3[/tex] and round to the nearest hundredth. [tex]2.8\times 13^{4x} +4.8 = 19.3[/tex][tex]2.8\times 13^{4x} = 19.3-4.8 [/tex][tex]2.8\times 13^{4x} = 14.5 [/tex][tex]13^{4x} = \frac{14.5}{2.8} [/tex][tex]13^{4x} = 5.17857142857 [/tex][tex]\log(13^{4x}) = \log(5.17857142857) [/tex][tex]4x \log(13) = \log(5.17857142857) [/tex][tex]4x = \frac{\log(5.17857142857)}{\log\left(13\right)} [/tex][tex]4x = 0.641154659628 [/tex][tex]x = \frac{0.641154659628}{4} [/tex][tex]x = 0.160288664907 [/tex]Round to the nearest hundredth. Hence final answer is approx x=0.16.