What is the answer to 1-8ln((2x-1)/7)=14 ?

The answer to 1-8ln((2x-1)/7)=14 is x=(7+e^{13/8})/(2e^{13/8)}

Solve for x: 1-8ln((2x-1)/7)=14

The solution is x=(7+e^{13/8})/(2e^{13/8)}

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1 - 8 ln (\frac{2 x - 1}{7}) = 14

x = \frac{7 + e ^{\frac{13}{8}}}{2 e ^{\frac{13}{8}}}

Decimal Notation

x = 1.18919 \dots

Solution steps

1 - 8 ln (\frac{2 x - 1}{7}) = 14

Move

1

to the right side

- 8 ln (\frac{2 x - 1}{7}) = 13

Divide both sides by

- 8

ln (\frac{2 x - 1}{7}) = - \frac{13}{8}

Apply log rules

\frac{2 x - 1}{7} = e^{- \frac{13}{8}}

Multiply both sides by

7

\frac{2 x - 1}{7} \cdot 7 = e^{- \frac{13}{8}} \cdot 7

Simplify

e^{- \frac{13}{8}} \cdot 7 : \frac{7}{e ^{\frac{13}{8}}}

2 x - 1 = \frac{7}{e ^{\frac{13}{8}}}

Solve

2 x - 1 = \frac{7}{e ^{\frac{13}{8}}} : x = \frac{7 + e ^{\frac{13}{8}}}{2 e ^{\frac{13}{8}}}

x = \frac{7 + e ^{\frac{13}{8}}}{2 e ^{\frac{13}{8}}}

Verify Solutions:

x = \frac{7 + e ^{\frac{13}{8}}}{2 e ^{\frac{13}{8}}}

True

The solution is

x = \frac{7 + e ^{\frac{13}{8}}}{2 e ^{\frac{13}{8}}}

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What is the answer to 1-8ln((2x-1)/7)=14 ?
The answer to 1-8ln((2x-1)/7)=14 is x=(7+e^{13/8})/(2e^{13/8)}
Solve for x: 1-8ln((2x-1)/7)=14
The solution is x=(7+e^{13/8})/(2e^{13/8)}