What is the answer to 5^b=25^b-1 ?

The answer to 5^b=25^b-1 is b=(ln((1+sqrt(5))/2))/(ln(5))

Solve for b: 5^b=25^b-1

The solution is b=(ln((1+sqrt(5))/2))/(ln(5))

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5^{b} = 2 5^{b} - 1

b = \frac{ln ( \frac{1 + 5}{2} )}{ln ( 5 )}

Decimal Notation

b = 0.29899 \dots

Solution steps

5^{b} = 2 5^{b} - 1

Apply exponent rules

5^{b} = (5^{b})^{2} - 1

Rewrite the equation with

5^{b} = u

u = (u)^{2} - 1

Solve

u = u^{2} - 1 : u = \frac{1 + 5}{2}, u = \frac{1 - 5}{2}

u = \frac{1 + 5}{2}, u = \frac{1 - 5}{2}

Substitute back

u = 5^{b},

solve for

b

Solve

5^{b} = \frac{1 + 5}{2} : b = \frac{ln ( \frac{1 + 5}{2} )}{ln ( 5 )}

Solve

5^{b} = \frac{1 - 5}{2} :

No Solution for

b \in R

b = \frac{ln ( \frac{1 + 5}{2} )}{ln ( 5 )}

2 e^{y} + 15 e^{- y} = 11

2.16 = (1 + 0.12)^{n - 1}

x^{a} = e^{x - 1}

y, \frac{x ^{- 2}}{x ^{y}} = \frac{1}{x ^{12}}

2^{2 x - 1} = 4^{x} - 2

What is the answer to 5^b=25^b-1 ?
The answer to 5^b=25^b-1 is b=(ln((1+sqrt(5))/2))/(ln(5))
Solve for b: 5^b=25^b-1
The solution is b=(ln((1+sqrt(5))/2))/(ln(5))