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Verified Answer :

InesWalston

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

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

\(\Rightarrow 4x=\ln \dfrac{5}{6}\)

\(\Rightarrow 4x=-0.1823\)

\(\Rightarrow x=\dfrac{-0.1823}{4}\)

\(\Rightarrow x=-0.0455\)

\(\Rightarrow x\approx -0.046\)

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