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2(4x-3)+log_(2)(3x+5)=3

$2(4 x-3)+\log _{2}(3 x+5)=3$

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Solve multi-step equations with fractional coefficients

Full solution

Q.

2(4 x-3)+\log _{2}(3 x+5)=3

Distribute and Simplify: Distribute the $2$ into the parentheses: $2(4x) - 2(3) + \log_{2}(3x+5) = 3$ . $\newline$ $8x - 6 + \log_{2}(3x+5) = 3$ .
Isolate Logarithmic Term: Add $6$ to both sides to isolate the logarithmic term: $8x + \log_{2}(3x+5) = 9$ .
Isolate $x$ : Divide both sides by $8$ to isolate $x$ on one side: $x + \left(\frac{1}{8}\right)\log_{2}(3x+5) = \frac{9}{8}$ .

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