What is the answer to 16^x+20^x-25^x=0 ?

The answer to 16^x+20^x-25^x=0 is x=(ln((1+sqrt(5))/2))/(ln(5/4))

Solve for x: 16^x+20^x-25^x=0

The solution is x=(ln((1+sqrt(5))/2))/(ln(5/4))

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1 6^{x} + 2 0^{x} - 2 5^{x} = 0

x = \frac{ln ( \frac{1 + 5}{2} )}{ln ( \frac{5}{4} )}

Decimal Notation

x = 2.15651 \dots

Solution steps

1 6^{x} + 2 0^{x} - 2 5^{x} = 0

Divide both sides by

1 6^{x}

\frac{1 6 ^{x}}{1 6 ^{x}} + \frac{2 0 ^{x}}{1 6 ^{x}} - \frac{2 5 ^{x}}{1 6 ^{x}} = \frac{0}{1 6 ^{x}}

Simplify

1 + (\frac{5}{4})^{x} - (\frac{25}{16})^{x} = 0

Apply exponent rules

1 + (\frac{5}{4})^{x} - ((\frac{5}{4})^{x})^{2} = 0

Rewrite the equation with

(\frac{5}{4})^{x} = u

1 + u - (u)^{2} = 0

Solve

1 + u - u^{2} = 0 : 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}{4})^{x},

solve for

x

Solve

(\frac{5}{4})^{x} = - \frac{- 1 + 5}{2} :

No Solution for

x \in R

Solve

(\frac{5}{4})^{x} = \frac{1 + 5}{2} : x = \frac{ln ( \frac{1 + 5}{2} )}{ln ( \frac{5}{4} )}

x = \frac{ln ( \frac{1 + 5}{2} )}{ln ( \frac{5}{4} )}

2 = 3^{x}

5^{x} + 5^{x + 1} + 5^{x - 2} + 5^{x - 3} = 780

ln (e^{x + 3}) = 10

3^{x} = \frac{1}{81}

3^{2 x} - 3^{x} - 72 = 0

What is the answer to 16^x+20^x-25^x=0 ?
The answer to 16^x+20^x-25^x=0 is x=(ln((1+sqrt(5))/2))/(ln(5/4))
Solve for x: 16^x+20^x-25^x=0
The solution is x=(ln((1+sqrt(5))/2))/(ln(5/4))