What is the answer to 36^x+42^x=49^x ?

The answer to 36^x+42^x=49^x is x=(ln((1+sqrt(5))/2))/(ln(7/6))

Solve for x: 36^x+42^x=49^x

The solution is x=(ln((1+sqrt(5))/2))/(ln(7/6))

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3 6^{x} + 4 2^{x} = 4 9^{x}

x = \frac{ln ( \frac{1 + 5}{2} )}{ln ( \frac{7}{6} )}

Decimal Notation

x = 3.12169 \dots

Solution steps

3 6^{x} + 4 2^{x} = 4 9^{x}

Divide both sides by

3 6^{x}

\frac{3 6 ^{x}}{3 6 ^{x}} + \frac{4 2 ^{x}}{3 6 ^{x}} = \frac{4 9 ^{x}}{3 6 ^{x}}

Simplify

1 + (\frac{7}{6})^{x} = (\frac{49}{36})^{x}

Apply exponent rules

1 + (\frac{7}{6})^{x} = ((\frac{7}{6})^{x})^{2}

Rewrite the equation with

(\frac{7}{6})^{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{7}{6})^{x},

solve for

x

Solve

(\frac{7}{6})^{x} = \frac{1 + 5}{2} : x = \frac{ln ( \frac{1 + 5}{2} )}{ln ( \frac{7}{6} )}

Solve

(\frac{7}{6})^{x} = \frac{1 - 5}{2} :

No Solution for

x \in R

x = \frac{ln ( \frac{1 + 5}{2} )}{ln ( \frac{7}{6} )}

5 \cdot 1 8^{6 x} = 26

5^{x} = 4

6^{x} = 216

3^{2 x + 2} + 3^{x + 3} - 10 = 0

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

What is the answer to 36^x+42^x=49^x ?
The answer to 36^x+42^x=49^x is x=(ln((1+sqrt(5))/2))/(ln(7/6))
Solve for x: 36^x+42^x=49^x
The solution is x=(ln((1+sqrt(5))/2))/(ln(7/6))