What is the answer to a^x=5+x ?

The answer to a^x=5+x is x=-(\W(-\frac{ln(a))/(a^5))+5ln(a)}{ln(a)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

a^x=5+x

a^{x} = 5 + x

x = - \frac{W ( - \frac{l n ( a )}{a ^{5}} ) + 5 ln ( a )}{ln ( a )}

Solution steps

a^{x} = 5 + x

Prepare

a^{x} = 5 + x

for Lambert form:

1 = (5 + x) e^{- x l n (a)}

Rewrite the equation with

(- x - 5) ln (a) = u

and

x = - \frac{u + 5 ln ( a )}{ln ( a )}

1 = (5 + (- \frac{u + 5 ln ( a )}{ln ( a )})) e^{- (- \frac{u + 5 l n ( a )}{l n ( a )}) l n (a)}

Simplify

1 = e^{u + 5 l n (a)} (5 - \frac{u + 5 ln ( a )}{ln ( a )})

Rewrite

1 = e^{u + 5 l n (a)} (5 - \frac{u + 5 ln ( a )}{ln ( a )})

in Lambert form:

e^{u} u = - \frac{ln ( a )}{a ^{5}}

Solve

e^{u} u = - \frac{ln ( a )}{a ^{5}} : u = W (- \frac{ln ( a )}{a ^{5}})

u = W (- \frac{ln ( a )}{a ^{5}})

Substitute back

u = (- x - 5) ln (a),

solve for

x

Solve

(- x - 5) ln (a) = W (- \frac{ln ( a )}{a ^{5}}) : x = - \frac{W ( - \frac{l n ( a )}{a ^{5}} ) + 5 ln ( a )}{ln ( a )}

x = - \frac{W ( - \frac{l n ( a )}{a ^{5}} ) + 5 ln ( a )}{ln ( a )}

1.0 5^{x} = 2

\frac{2 ^{2 n - 1}}{4} = 8^{3}

14800 = 7400 \cdot (1 + (\frac{3}{100}))^{x}

(m - 2)^{m - 2} = 14 4^{6}

2^{x} - 2 + 2^{3} - x = 3

What is the answer to a^x=5+x ?
The answer to a^x=5+x is x=-(\W(-\frac{ln(a))/(a^5))+5ln(a)}{ln(a)}