Question

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

Answer 1

Answer:

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

Step-by-step explanation:

The given equation is,

$\Rightarrow 6e^{4x} - 2 = 3$

$\Rightarrow 6e^{4x}= 3+2$

$\Rightarrow 6e^{4x}=5$

$\Rightarrow e^{4x}=\dfrac{5}{6}$

Taking natural logarithms of both side,

$\Rightarrow \ln e^{4x}=\ln \dfrac{5}{6}$

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

$\Rightarrow 4x\times \ln e=\ln \dfrac{5}{6}$

As, $\ln e = 1$, so

$\Rightarrow 4x\times 1=\ln \dfrac{5}{6}$

$\Rightarrow 4x=\ln \dfrac{5}{6}$

$\Rightarrow 4x=-0.1823$

$\Rightarrow x=\dfrac{-0.1823}{4}$

$\Rightarrow x=-0.0455$

$\Rightarrow x\approx -0.046$