en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

e^x+15e^{-x}=8

Solution

e^{x} + 15 e^{- x} = 8

Solution

x = ln (5), x = ln (3)

+1

Decimal Notation

x = 1.60943 \dots, x = 1.09861 \dots

Solution steps

e^{x} + 15 e^{- x} = 8

Apply exponent rules

e^{x} + 15 (e^{x})^{- 1} = 8

Rewrite the equation with

e^{x} = u

u + 15 (u)^{- 1} = 8

Solve

u + 15 u^{- 1} = 8 : u = 5, u = 3

u = 5, u = 3

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 5 : x = ln (5)

Solve

e^{x} = 3 : x = ln (3)

x = ln (5), x = ln (3)

Popular Examples

2^{2+y}-2^{1+y}=2^4

2^{2 + y} - 2^{1 + y} = 2^{4}

solvefor x,-4^{2y}=3^{8x}solve for

x, - 4^{2 y} = 3^{8 x}

993=10^{((1.25-m+5))/5}

993 = 1 0^{\frac{( 1.25 - m + 5 )}{5}}

2 = 1.0 6^{n}

5e^x+48e^{-x}=46

5 e^{x} + 48 e^{- x} = 46

Frequently Asked Questions (FAQ)

What is the answer to e^x+15e^{-x}=8 ?
The answer to e^x+15e^{-x}=8 is x=ln(5),x=ln(3)