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

\[6e ^{4x-2}=3\]
\[e ^{4x-2}=\frac{ 3 }{6 }=\frac{ 1 }{ 2 }\]
\[\ln e ^{4x-2}=\ln \frac{ 1 }{ 2 }=\ln 1-\ln 2 =0-\ln 2\]
\[\left( 4x-2 \right)\ln e=-\ln 2\]
\[4x-2=-\ln 2 \left(\because \ln e=1 \right)\]
\[4x=2-\ln 2\]
\[x=\frac{ 1 }{2 }-\frac{ 1 }{ 4 }\ln 2\]
after substituting the value of log2 from the calculator or log tables you can find the value of x

Answer 2

thank you so much

Answer 3

the answer is A