What is the answer to 4^x+6^x-2*9^x=0 ?

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

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4^x+6^x-2*9^x=0

4^{x} + 6^{x} - 2 \cdot 9^{x} = 0

x = 0

Solution steps

4^{x} + 6^{x} - 2 \cdot 9^{x} = 0

Divide both sides by

4^{x}

\frac{4 ^{x}}{4 ^{x}} + \frac{6 ^{x}}{4 ^{x}} - \frac{2 \cdot 9 ^{x}}{4 ^{x}} = \frac{0}{4 ^{x}}

Simplify

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

1 + (\frac{3}{2})^{x} - \frac{2 \cdot 9 ^{x}}{4 ^{x}} = 0

Apply exponent rules

1 + (4^{x})^{0.29248 \dots} - \frac{2 ( 4 ^{x} ) ^{1.58496 \dots}}{4 ^{x}} = 0

Rewrite the equation with

4^{x} = u

1 + (u)^{0.29248 \dots} - \frac{2 ( u ) ^{1.58496 \dots}}{u} = 0

Solve

1 + u^{0.29248 \dots} - \frac{2 u ^{1.58496 \dots}}{u} = 0 : u = 1

u = 1

Substitute back

u = 4^{x},

solve for

x

Solve

4^{x} = 1 : x = 0

x = 0

2 7^{x + 3} = 9^{2 x}

7^{2 x + 4} = 3^{5 x + 7}

4^{x^{2}} \cdot 4^{x} = 4^{0}

4^{x + 1} - 7 (2^{x}) = 2

x, 2^{π + 3 x} = 4^{2 y + 1}