`3^(x+4) = 6^(2x-5)`
To solve, take the natural logarithm of both sides.
`ln (3^(x+4)) = ln (6^(2x-5))`
To simplify each side, apply the logarithm rule `ln (a^m) =m*ln(a)` .
`(x+4)ln(3) = (2x-5) ln (6)`
`xln(3)+4ln(3) = 2xln(6) - 5ln(6)`
Then, bring together the terms with x on one side of the equation. Also, bring together the terms without x on the other side of the equation.
`xln(3) - 2xln(6) = -4ln(3) -5ln(6)`
At the left...
`3^(x+4) = 6^(2x-5)`
To solve, take the natural logarithm of both sides.
`ln (3^(x+4)) = ln (6^(2x-5))`
To simplify each side, apply the logarithm rule `ln (a^m) =m*ln(a)` .
`(x+4)ln(3) = (2x-5) ln (6)`
`xln(3)+4ln(3) = 2xln(6) - 5ln(6)`
Then, bring together the terms with x on one side of the equation. Also, bring together the terms without x on the other side of the equation.
`xln(3) - 2xln(6) = -4ln(3) -5ln(6)`
At the left side, factor out the GCF.
`x(ln(3) - 2ln(6)) =-4ln(3) -5ln(6)`
And, isolate the x.
`x = (-4ln(3) - 5ln(6))/(ln(3)-2ln(6))`
`x~~5.374`
Therefore, the solution is `x~~5.374` .
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