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Popular >

5^x=-x+6

Solution

5^{x} = - x + 6

Solution

x = 1

Solution steps

5^{x} = - x + 6

Prepare

5^{x} = - x + 6

for Lambert form:

1 = (- x + 6) e^{- l n (5) x}

Rewrite the equation with

(- x + 6) ln (5) = u

and

x = - \frac{u - 6 ln ( 5 )}{ln ( 5 )}

1 = (- (- \frac{u - 6 ln ( 5 )}{ln ( 5 )}) + 6) e^{- l n (5) (- \frac{u - 6 l n ( 5 )}{l n ( 5 )})}

Simplify

1 = e^{u - 6 l n (5)} (\frac{u - 6 ln ( 5 )}{ln ( 5 )} + 6)

Rewrite

1 = e^{u - 6 l n (5)} (\frac{u - 6 ln ( 5 )}{ln ( 5 )} + 6)

in Lambert form:

e^{u} u = 15625 ln (5)

Solve

e^{u} u = 15625 ln (5) : u = 5 ln (5)

u = 5 ln (5)

Substitute back

u = (- x + 6) ln (5),

solve for

x

Solve

(- x + 6) ln (5) = 5 ln (5) : x = 1

x = 1

Popular Examples

2 - e^{x} = 0

67 = 1 5^{x}

(3)^{x} = 81

2 e^{x} - 1 = 0

solvefor x,2^x+3^y=41 solve for

x, 2^{x} + 3^{y} = 41

Frequently Asked Questions (FAQ)

What is the answer to 5^x=-x+6 ?
The answer to 5^x=-x+6 is x=1
Solve for x: 5^x=-x+6
The solution is x=1