What is the answer to 3^{5^x}=5^{3^x} ?

The answer to 3^{5^x}=5^{3^x} is x=(ln(ln(5))-ln(ln(3)))/(ln(5)-ln(3))

Solve for x: 3^{5^x}=5^{3^x}

The solution is x=(ln(ln(5))-ln(ln(3)))/(ln(5)-ln(3))

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3^{5^{x}} = 5^{3^{x}}

x = \frac{ln ( ln ( 5 ) ) - ln ( ln ( 3 ) )}{ln ( 5 ) - ln ( 3 )}

Decimal Notation

x = 0.74749 \dots

Solution steps

3^{5^{x}} = 5^{3^{x}}

Apply exponent rules

x ln (5) + ln (ln (3)) = x ln (3) + ln (ln (5))

Solve

x ln (5) + ln (ln (3)) = x ln (3) + ln (ln (5)) : x = \frac{ln ( ln ( 5 ) ) - ln ( ln ( 3 ) )}{ln ( 5 ) - ln ( 3 )}

x = \frac{ln ( ln ( 5 ) ) - ln ( ln ( 3 ) )}{ln ( 5 ) - ln ( 3 )}

2 7^{x + 4} = (\frac{1}{9})^{x - 1}

3 2^{2 c} = 8^{c + 7}

1 0^{x} = 1000000

y, x^{y} = x y

2^{x + \frac{9}{2}} = 42

What is the answer to 3^{5^x}=5^{3^x} ?
The answer to 3^{5^x}=5^{3^x} is x=(ln(ln(5))-ln(ln(3)))/(ln(5)-ln(3))
Solve for x: 3^{5^x}=5^{3^x}
The solution is x=(ln(ln(5))-ln(ln(3)))/(ln(5)-ln(3))