What is the answer to 2^x*27=3^x ?

The answer to 2^x*27=3^x is x=(3ln(3))/(ln(3)-ln(2))

Solve for x: 2^x*27=3^x

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

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2^{x} \cdot 27 = 3^{x}

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

Decimal Notation

x = 8.12853 \dots

Solution steps

2^{x} \cdot 27 = 3^{x}

Apply exponent rules

x ln (2) + ln (27) = x ln (3)

Solve

x ln (2) + ln (27) = x ln (3) : x = \frac{3 ln ( 3 )}{ln ( 3 ) - ln ( 2 )}

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

1 6^{x - 3} = 1 6^{2 x - 1}

x, 1 - (1 - 0.01)^{x} = 0.01

3^{2 x} - 3^{x + 1} - 4 = 0

2 = (5)^{\frac{x}{20}}

5 e^{x + 1} = 2

What is the answer to 2^x*27=3^x ?
The answer to 2^x*27=3^x is x=(3ln(3))/(ln(3)-ln(2))
Solve for x: 2^x*27=3^x
The solution is x=(3ln(3))/(ln(3)-ln(2))