What is the answer to ln(13e^{4x})=ln(2) ?

The answer to ln(13e^{4x})=ln(2) is x=(ln(2/13))/4

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ln(13e^{4x})=ln(2)

ln (13 e^{4 x}) = ln (2)

x = \frac{ln ( \frac{2}{13} )}{4}

Decimal Notation

x = - 0.46795 \dots

Solution steps

ln (13 e^{4 x}) = ln (2)

Rewrite the equation with

e^{4 x} = u

ln (13 u) = ln (2)

Solve

ln (13 u) = ln (2) : u = \frac{2}{13}

u = \frac{2}{13}

Substitute back

u = e^{4 x},

solve for

x

Solve

e^{4 x} = \frac{2}{13} : x = \frac{ln ( \frac{2}{13} )}{4}

x = \frac{ln ( \frac{2}{13} )}{4}

5^{x} + 5^{3 x} = 10

4 x - 3 = e^{x - 3} + 1

5^{3 x - 7} + 11 = 16

6^{x} = \frac{1}{1296}

7^{8 x + 7} = 2

What is the answer to ln(13e^{4x})=ln(2) ?
The answer to ln(13e^{4x})=ln(2) is x=(ln(2/13))/4