What is the answer to 3^{x+2}=10^x ?

The answer to 3^{x+2}=10^x is x=(2ln(3))/(ln(10)-ln(3))

Solve for x: 3^{x+2}=10^x

The solution is x=(2ln(3))/(ln(10)-ln(3))

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

x = \frac{2 ln ( 3 )}{ln ( 10 ) - ln ( 3 )}

Decimal Notation

x = 1.82497 \dots

Solution steps

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

Apply exponent rules

(x + 2) ln (3) = x ln (10)

Solve

(x + 2) ln (3) = x ln (10) : x = \frac{2 ln ( 3 )}{ln ( 10 ) - ln ( 3 )}

x = \frac{2 ln ( 3 )}{ln ( 10 ) - ln ( 3 )}

2^{(2 x + 3)} = 3^{3 x}

5^{x} = 3125

3^{2 x + 1} - 10 (3^{x}) + 3 = 0

(\frac{1}{2})^{x} = 2

3^{x} = - 2

What is the answer to 3^{x+2}=10^x ?
The answer to 3^{x+2}=10^x is x=(2ln(3))/(ln(10)-ln(3))
Solve for x: 3^{x+2}=10^x
The solution is x=(2ln(3))/(ln(10)-ln(3))