Question

Use natural logarithms to solve the equation. Round to the nearest thousandth.

6e4x - 2 = 3

A. –0.448

B. 0.327

C. 0.067

D. –0.046

Answer 1

`\boxed{\boxed{x=-0.046}}`

Explanation:

The given equation is,

`\Rightarrow 6e^(4x) - 2 = 3`

`\Rightarrow 6e^(4x)= 3+2`

`\Rightarrow 6e^(4x)=5`

`\Rightarrow e^(4x)=(5)/(6)`

Taking natural logarithms of both side,

`\Rightarrow \ln e^(4x)=\ln (5)/(6)`

As,
`\log a^b=b\log a`, so

`\Rightarrow 4x* \ln e=\ln (5)/(6)`

As,
`\ln e = 1`, so

`\Rightarrow 4x* 1=\ln (5)/(6)`

`\Rightarrow 4x=\ln (5)/(6)`

`\Rightarrow 4x=-0.1823`

`\Rightarrow x=(-0.1823)/(4)`

`\Rightarrow x=-0.0455`

`\Rightarrow x\approx -0.046`