What is the answer to 3^{x+1/2}\times 3^{x-2}=1 ?

The answer to 3^{x+1/2}\times 3^{x-2}=1 is x= 3/4

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3^{x+1/2}\times 3^{x-2}=1

3^{x + \frac{1}{2}} \cdot 3^{x - 2} = 1

x = \frac{3}{4}

Decimal Notation

x = 0.75

Solution steps

3^{x + \frac{1}{2}} \cdot 3^{x - 2} = 1

Apply exponent rules

(x + \frac{1}{2} + x - 2) ln (3) = ln (1)

Solve

(x + \frac{1}{2} + x - 2) ln (3) = ln (1) : x = \frac{3}{4}

x = \frac{3}{4}

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

2^{3 k - 1} \cdot 2^{5 k - 7} = 16

4^{2 x} = 62 5^{3 x + 5}

\frac{1}{2} = 1 - e^{- 2 x}

7^{x - 1} = 49

What is the answer to 3^{x+1/2}\times 3^{x-2}=1 ?
The answer to 3^{x+1/2}\times 3^{x-2}=1 is x= 3/4
Solve for x: 3^{x+1/2}\times 3^{x-2}=1
The solution is x= 3/4