Solve the equation. Round to the nearest hundredth. Show work. 1.2 · 10x{4x} - 4.2 = 9.9

Question

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


`1.2` ·
`10x{4x} - 4.2 = 9.9`

Answer 1

x=0.27

Explanation:

We are given the equation;

`1.2*10^(4x)-4.2=9.9`

The first step is to add 4.2 on both sides of the equation;

`1.2*10^(4x)=14.1`

The next step will be to divide both sides of the equation by 1.2;

`10^(4x)=11.75`

Next we take natural logs on both sides of the equation;

`(4x)ln10=ln11.75`

Finally, we divide both sides by 4*ln10 and simplify to determine x;

`x=(ln11.75)/(4ln10)=0.27`