What is the answer to 25^x+30^x=36^x ?

The answer to 25^x+30^x=36^x is x=(ln((1+sqrt(5))/2))/(ln(6/5))

Solve for x: 25^x+30^x=36^x

The solution is x=(ln((1+sqrt(5))/2))/(ln(6/5))

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2 5^{x} + 3 0^{x} = 3 6^{x}

x = \frac{ln ( \frac{1 + 5}{2} )}{ln ( \frac{6}{5} )}

Decimal Notation

x = 2.63935 \dots

Solution steps

2 5^{x} + 3 0^{x} = 3 6^{x}

Divide both sides by

2 5^{x}

\frac{2 5 ^{x}}{2 5 ^{x}} + \frac{3 0 ^{x}}{2 5 ^{x}} = \frac{3 6 ^{x}}{2 5 ^{x}}

Simplify

1 + (\frac{6}{5})^{x} = (\frac{36}{25})^{x}

Apply exponent rules

1 + (\frac{6}{5})^{x} = ((\frac{6}{5})^{x})^{2}

Rewrite the equation with

(\frac{6}{5})^{x} = u

1 + u = (u)^{2}

Solve

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

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

Substitute back

u = (\frac{6}{5})^{x},

solve for

x

Solve

(\frac{6}{5})^{x} = \frac{1 + 5}{2} : x = \frac{ln ( \frac{1 + 5}{2} )}{ln ( \frac{6}{5} )}

Solve

(\frac{6}{5})^{x} = \frac{1 - 5}{2} :

No Solution for

x \in R

x = \frac{ln ( \frac{1 + 5}{2} )}{ln ( \frac{6}{5} )}

9^{x} = 27

x, x^{y} = y^{x}

e^{x} = 2 - x

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

e^{x} = 7

What is the answer to 25^x+30^x=36^x ?
The answer to 25^x+30^x=36^x is x=(ln((1+sqrt(5))/2))/(ln(6/5))
Solve for x: 25^x+30^x=36^x
The solution is x=(ln((1+sqrt(5))/2))/(ln(6/5))