What is the answer to 3^{x-2}=7^x ?

The answer to 3^{x-2}=7^x is x=(2ln(3))/(ln(3)-ln(7))

Solve for x: 3^{x-2}=7^x

The solution is x=(2ln(3))/(ln(3)-ln(7))

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

x = \frac{2 ln ( 3 )}{ln ( 3 ) - ln ( 7 )}

Decimal Notation

x = - 2.59321 \dots

Solution steps

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

Apply exponent rules

(x - 2) ln (3) = x ln (7)

Solve

(x - 2) ln (3) = x ln (7) : x = \frac{2 ln ( 3 )}{ln ( 3 ) - ln ( 7 )}

x = \frac{2 ln ( 3 )}{ln ( 3 ) - ln ( 7 )}

5^{2 x} = 5^{7 x - 1}

(0.3)^{1 + x} = 1. 7^{2 x - 1}

4^{2 x - 1} + 4^{2 x} = 4

3 2^{2 x + 3} = 1 6^{x + 4}

3 (2^{2 x + 3}) - 43 (2^{x}) + 5 = 0

What is the answer to 3^{x-2}=7^x ?
The answer to 3^{x-2}=7^x is x=(2ln(3))/(ln(3)-ln(7))
Solve for x: 3^{x-2}=7^x
The solution is x=(2ln(3))/(ln(3)-ln(7))