What is the answer to 81^{x^2}=27^x ?

The answer to 81^{x^2}=27^x is x=0,x= 3/4

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81^{x^2}=27^x

8 1^{x^{2}} = 2 7^{x}

x = 0, x = \frac{3}{4}

Decimal

x = 0, x = 0.75

Solution steps

8 1^{x^{2}} = 2 7^{x}

Apply exponent rules

4 x^{2} = 3 x

Solve

4 x^{2} = 3 x : x = 0, x = \frac{3}{4}

x = 0, x = \frac{3}{4}

4^{x} = 47

4^{x} = 27

n, (x^{3})^{3} = x^{n}

4^{x} \times 3^{2 x} = 6

5 x = 4^{x + 1}