What is the answer to 81^{3^{2x}}=27^{4^{2x}} ?

The answer to 81^{3^{2x}}=27^{4^{2x}} is x= 1/2

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81^{3^{2x}}=27^{4^{2x}}

8 1^{3^{2 x}} = 2 7^{4^{2 x}}

x = \frac{1}{2}

Decimal Notation

x = 0.5

Solution steps

8 1^{3^{2 x}} = 2 7^{4^{2 x}}

Apply exponent rules

ln (4) + 2 x ln (3) = ln (3) + 2 x ln (4)

Solve

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

x = \frac{1}{2}

9^{2 x} = 27

2^{2 x - 1} - 6 \cdot 2^{x - 1} + 4 = 0

3 2^{x} = 2

3^{15 x - 73} = 3^{7 x - 1}

2^{4 - 3 x} = 1 6^{\frac{2}{5}}

What is the answer to 81^{3^{2x}}=27^{4^{2x}} ?
The answer to 81^{3^{2x}}=27^{4^{2x}} is x= 1/2
Solve for x: 81^{3^{2x}}=27^{4^{2x}}
The solution is x= 1/2