What is the answer to 25^x-15^x=9^x ?

The answer to 25^x-15^x=9^x is x=(ln((1+sqrt(5))/2))/(ln(5/3))

Solve for x: 25^x-15^x=9^x

The solution is x=(ln((1+sqrt(5))/2))/(ln(5/3))

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2 5^{x} - 1 5^{x} = 9^{x}

x = \frac{ln ( \frac{1 + 5}{2} )}{ln ( \frac{5}{3} )}

Decimal

x = 0.94202 \dots

Solution steps

2 5^{x} - 1 5^{x} = 9^{x}

Divide both sides by

9^{x}

\frac{2 5 ^{x}}{9 ^{x}} - \frac{1 5 ^{x}}{9 ^{x}} = \frac{9 ^{x}}{9 ^{x}}

Simplify

(\frac{25}{9})^{x} - (\frac{5}{3})^{x} = 1

Apply exponent rules

((\frac{5}{3})^{x})^{2} - (\frac{5}{3})^{x} = 1

Rewrite the equation with

(\frac{5}{3})^{x} = u

(u)^{2} - u = 1

Solve

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

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

Substitute back

u = (\frac{5}{3})^{x},

solve for

x

Solve

(\frac{5}{3})^{x} = \frac{1 + 5}{2} : x = \frac{ln ( \frac{1 + 5}{2} )}{ln ( \frac{5}{3} )}

Solve

(\frac{5}{3})^{x} = \frac{1 - 5}{2} :

No Solution for

x \in R

x = \frac{ln ( \frac{1 + 5}{2} )}{ln ( \frac{5}{3} )}

y, x = e^{3 y}

5^{x} + 8 = 26

2400 (1 - e^{3 x}) = 2000

0 = 2 e^{2 x} - 3 e^{1 - 3 x}

4 x^{2} e^{- 2 x} - 8 x e^{- 2 x} + 2 e^{- 2 x} = 0

What is the answer to 25^x-15^x=9^x ?
The answer to 25^x-15^x=9^x is x=(ln((1+sqrt(5))/2))/(ln(5/3))
Solve for x: 25^x-15^x=9^x
The solution is x=(ln((1+sqrt(5))/2))/(ln(5/3))