What is the answer to 9^x+3=4(3^x) ?

The answer to 9^x+3=4(3^x) is x=1,x=0

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9^x+3=4(3^x)

9^{x} + 3 = 4 (3^{x})

x = 1, x = 0

Solution steps

9^{x} + 3 = 4 (3^{x})

Apply exponent rules

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

Rewrite the equation with

3^{x} = u

(u)^{2} + 3 = 4 u

Solve

u^{2} + 3 = 4 u : u = 3, u = 1

u = 3, u = 1

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 3 : x = 1

Solve

3^{x} = 1 : x = 0

x = 1, x = 0

0 = 3 - 2^{x}

\frac{e ^{5 x}}{e ^{- 3 x + 1}} - 8 = 0

- 6^{x} = - \frac{1}{36}

y, x = e^{y^{3}}

2^{x^{2} - x} = 64