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To solve $\frac{2}{3}x=12$ we multiply both sides by $\frac{2}{3}$

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Solve logarithmic equations with one logarithm

Full solution

Q. To solve

\frac{2}{3}x=12

we multiply both sides by

\frac{2}{3}

Understand and Identify Operation: Understand the equation and identify the operation needed to isolate $x$ . The equation is $\frac{2}{3}x = 12$ , and we want to find the value of $x$ . To do this, we need to get $x$ by itself on one side of the equation. This means we need to undo the multiplication of $x$ by $\frac{2}{3}$ . The inverse operation of multiplying by $\frac{2}{3}$ is dividing by $\frac{2}{3}$ , which is the same as multiplying by the reciprocal, $\frac{3}{2}$ .
Multiply by Reciprocal: Multiply both sides of the equation by the reciprocal of $\frac{2}{3}$ , which is $\frac{3}{2}$ . $\left(\frac{3}{2}\right) \times \left(\frac{2}{3}x\right) = \left(\frac{3}{2}\right) \times 12$
Simplify Left Side: Simplify the left side of the equation by canceling out the $\frac{2}{3}$ with its reciprocal $\frac{3}{2}$ . The $2$ in the numerator of $\frac{3}{2}$ cancels with the $2$ in the denominator of $\frac{2}{3}$ , and the $3$ in the denominator of $\frac{3}{2}$ cancels with the $3$ in the numerator of $\frac{2}{3}$ , leaving us with $\frac{3}{2}$ $0$ on the left side. $\frac{3}{2}$ $1$
Perform Multiplication: Perform the multiplication on the right side of the equation. $\newline$ $x = \frac{3}{2} \times 12$ $\newline$ $x = 3 \times 6$ $\newline$ $x = 18$

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