What is the answer to sqrt(7\sqrt{7\sqrt{7)}}=343^x ?

The answer to sqrt(7\sqrt{7\sqrt{7)}}=343^x is x= 7/24

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sqrt(7\sqrt{7\sqrt{7)}}=343^x

777 = 34 3^{x}

x = \frac{7}{24}

Decimal Notation

x = 0.29166 \dots

Solution steps

777 = 34 3^{x}

Apply exponent rules

\frac{7}{24} = x

Switch sides

x = \frac{7}{24}

x^{x + 1} = x^{2 - x}

3^{2 x + 1} = 2^{x - 2}

2 7^{x} = \frac{9}{( 3 ^{x} )}

3^{x} = 6

3^{x} = 5

What is the answer to sqrt(7\sqrt{7\sqrt{7)}}=343^x ?
The answer to sqrt(7\sqrt{7\sqrt{7)}}=343^x is x= 7/24
Solve for x: sqrt(7\sqrt{7\sqrt{7)}}=343^x
The solution is x= 7/24