What is the answer to ln(8/(e^{4x)})=24 ?

The answer to ln(8/(e^{4x)})=24 is x=-(24-3ln(2))/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

ln(8/(e^{4x)})=24

ln (\frac{8}{e ^{4 x}}) = 24

x = - \frac{24 - 3 ln ( 2 )}{4}

Decimal Notation

x = - 5.48013 \dots

Solution steps

ln (\frac{8}{e ^{4 x}}) = 24

Apply exponent rules

ln (8 e^{- 4 x}) = 24

Rewrite the equation with

e^{- 4 x} = u

ln (8 u) = 24

Solve

ln (8 u) = 24 : u = \frac{e ^{24}}{8}

u = \frac{e ^{24}}{8}

Substitute back

u = e^{- 4 x},

solve for

x

Solve

e^{- 4 x} = \frac{e ^{24}}{8} : x = - \frac{24 - 3 ln ( 2 )}{4}

x = - \frac{24 - 3 ln ( 2 )}{4}

Verify Solutions:

x = - \frac{24 - 3 ln ( 2 )}{4}

True

The solution is

x = - \frac{24 - 3 ln ( 2 )}{4}

9^{2 x - 1} = \frac{1}{81}

e^{m x} (m^{2} + 6 m + 5) = 0

4^{8^{3 + 2 x}} = 2^{2^{7 x - 1}}

2 \cdot 3^{\frac{x}{5}} = 1

9^{x + 2} = 8 1^{3 x - 1}

What is the answer to ln(8/(e^{4x)})=24 ?
The answer to ln(8/(e^{4x)})=24 is x=-(24-3ln(2))/4