What is the answer to 4^x+6^x=2*9^x ?

The answer to 4^x+6^x=2*9^x is x=0

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4^x+6^x=2*9^x

4^{x} + 6^{x} = 2 \cdot 9^{x}

x = 0

Solution steps

4^{x} + 6^{x} = 2 \cdot 9^{x}

Divide both sides by

4^{x}

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

Simplify

\frac{6 ^{x}}{4 ^{x}} : (\frac{3}{2})^{x}

1 + (\frac{3}{2})^{x} = \frac{2 \cdot 9 ^{x}}{4 ^{x}}

Apply exponent rules

1 + (4^{x})^{0.29248 \dots} = \frac{2 ( 4 ^{x} ) ^{1.58496 \dots}}{4 ^{x}}

Rewrite the equation with

4^{x} = u

1 + (u)^{0.29248 \dots} = \frac{2 ( u ) ^{1.58496 \dots}}{u}

Solve

1 + u^{0.29248 \dots} = \frac{2 u ^{1.58496 \dots}}{u} : u = 1

u = 1

Substitute back

u = 4^{x},

solve for

x

Solve

4^{x} = 1 : x = 0

x = 0

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

1 6^{2 x + 1} = 3^{3 x - 4}

(- 4)^{x} = \frac{1}{16}

1 = 3^{x}

e^{2 x} + e^{x} - 6 = 0