What is the answer to 3^{x+2}=sqrt(5^x) ?

The answer to 3^{x+2}=sqrt(5^x) is x=-(4ln(3))/(2ln(3)-ln(5))

Solve for x: 3^{x+2}=sqrt(5^x)

The solution is x=-(4ln(3))/(2ln(3)-ln(5))

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3^{x + 2} = 5^{x}

x = - \frac{4 ln ( 3 )}{2 ln ( 3 ) - ln ( 5 )}

Decimal Notation

x = - 7.47626 \dots

Solution steps

3^{x + 2} = 5^{x}

Apply exponent rules

(x + 2) ln (3) = x \frac{1}{2} ln (5)

Solve

(x + 2) ln (3) = x \frac{1}{2} ln (5) : x = - \frac{4 ln ( 3 )}{2 ln ( 3 ) - ln ( 5 )}

x = - \frac{4 ln ( 3 )}{2 ln ( 3 ) - ln ( 5 )}

2^{x - 2} = 4

lo g_{10} (2^{x}) = \frac{3}{2}

5^{x^{2}} = 2 5^{x}

2^{x} = \frac{4 ^{7}}{8 ^{3}}

(\frac{1}{8})^{2 - 3 x} = 3 2^{4 + x}

What is the answer to 3^{x+2}=sqrt(5^x) ?
The answer to 3^{x+2}=sqrt(5^x) is x=-(4ln(3))/(2ln(3)-ln(5))
Solve for x: 3^{x+2}=sqrt(5^x)
The solution is x=-(4ln(3))/(2ln(3)-ln(5))