Solve for the exact value of x. log_(3)(6x)+log_(3)(2)=3 Answer:

Combine Logarithms: Combine the logarithms using the product rule. The product rule of logarithms states that log_b(m) + log_b(n) = log_b(m*n). Let's apply this rule to combine the two logarithms on the left side of the equation. log_3(6x) + log_3(2) = log_3(6x * 2) Simplify the product inside the logarithm. log_3(12x) = 3Simplify Product: Convert the logarithmic equation to an exponential equation. The definition of a logarithm states that if log_b(a) = c, then b^c = a. We will use this definition to rewrite the equation in exponential form. 3^3 = 12x Calculate the value of 3^3. 27 = 12xConvert to Exponential: Solve for x. To find the value of x, divide both sides of the equation by 12. 27 / 12 = x Simplify the fraction. x = 27 / 12 x = 9 / 4 x = 2.25

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Solve for the exact value of
x.

log_(3)(6x)+log_(3)(2)=3
Answer:

Solve for the exact value of $x$ . $\newline$ $\log _{3}(6 x)+\log _{3}(2)=3$ $\newline$ Answer:

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Precalculus

Quotient property of logarithms

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Q. Solve for the exact value of

x

\newline

\log _{3}(6 x)+\log _{3}(2)=3

\newline

Answer:

Combine Logarithms: Combine the logarithms using the product rule. $\newline$ The product rule of logarithms states that $\log_b(m) + \log_b(n) = \log_b(m*n)$ . Let's apply this rule to combine the two logarithms on the left side of the equation. $\newline$ $\log_3(6x) + \log_3(2) = \log_3(6x \cdot 2)$ $\newline$ Simplify the product inside the logarithm. $\newline$ $\log_3(12x) = 3$
Simplify Product: Convert the logarithmic equation to an exponential equation. $\newline$ The definition of a logarithm states that if $\log_b(a) = c$ , then $b^c = a$ . We will use this definition to rewrite the equation in exponential form. $\newline$ $3^3 = 12x$ $\newline$ Calculate the value of $3^3$ . $\newline$ $27 = 12x$
Convert to Exponential: Solve for $x$ . $\newline$ To find the value of $x$ , divide both sides of the equation by $12$ . $\newline$ $\frac{27}{12} = x$ $\newline$ Simplify the fraction. $\newline$ $x = \frac{27}{12}$ $\newline$ $x = \frac{9}{4}$ $\newline$ $x = 2.25$