What is the answer to 125^{log_{3}(x+3)}=8 ?

The answer to 125^{log_{3}(x+3)}=8 is x=3^{(ln(2))/(ln(5))}-3

Solve for x: 125^{log_{3}(x+3)}=8

The solution is x=3^{(ln(2))/(ln(5))}-3

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12 5^{l o g_{3} (x + 3)} = 8

x = 3^{\frac{l n ( 2 )}{l n ( 5 )}} - 3

Decimal

x = - 1.39496 \dots

Solution steps

12 5^{l o g_{3} (x + 3)} = 8

Apply exponent rules

lo g_{3} (x + 3) ln (125) = ln (8)

Solve

lo g_{3} (x + 3) ln (125) = ln (8) : x = 3^{\frac{l n ( 2 )}{l n ( 5 )}} - 3

x = 3^{\frac{l n ( 2 )}{l n ( 5 )}} - 3

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

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

2^{x} - 2^{- x} = 5 (1 - 2^{- x})

3^{x - 2} \cdot 2^{x - 1} = 1125

4^{x} = (2^{x})^{2}

What is the answer to 125^{log_{3}(x+3)}=8 ?
The answer to 125^{log_{3}(x+3)}=8 is x=3^{(ln(2))/(ln(5))}-3
Solve for x: 125^{log_{3}(x+3)}=8
The solution is x=3^{(ln(2))/(ln(5))}-3