What is the answer to 0.4^{x-1}=6.25^{6x-5} ?

The answer to 0.4^{x-1}=6.25^{6x-5} is x=(5ln(6.25)-ln(0.4))/(6ln(6.25)-ln(0.4))

Solve for x: 0.4^{x-1}=6.25^{6x-5}

The solution is x=(5ln(6.25)-ln(0.4))/(6ln(6.25)-ln(0.4))

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0. 4^{x - 1} = 6.2 5^{6 x - 5}

x = \frac{5 ln ( 6.25 ) - ln ( 0.4 )}{6 ln ( 6.25 ) - ln ( 0.4 )}

Decimal Notation

x = 0.84615 \dots

Solution steps

0. 4^{x - 1} = 6.2 5^{6 x - 5}

Apply exponent rules

(x - 1) ln (0.4) = (6 x - 5) ln (6.25)

Solve

(x - 1) ln (0.4) = (6 x - 5) ln (6.25) : x = \frac{5 ln ( 6.25 ) - ln ( 0.4 )}{6 ln ( 6.25 ) - ln ( 0.4 )}

x = \frac{5 ln ( 6.25 ) - ln ( 0.4 )}{6 ln ( 6.25 ) - ln ( 0.4 )}

e^{x} x - e^{x} = 0

1 + 2 e^{2 l n (x)} = 7

e^{x - 9} = 73

e^{0.4 x} = 8

1 6^{2 x - 3} = 8^{3 x + 4}

What is the answer to 0.4^{x-1}=6.25^{6x-5} ?
The answer to 0.4^{x-1}=6.25^{6x-5} is x=(5ln(6.25)-ln(0.4))/(6ln(6.25)-ln(0.4))
Solve for x: 0.4^{x-1}=6.25^{6x-5}
The solution is x=(5ln(6.25)-ln(0.4))/(6ln(6.25)-ln(0.4))