Solve for the exact value of x. log_(4)(3x)-2log_(4)(2)=2 Answer:

Apply Power Rule: Let's start by applying the power rule of logarithms to the term with the coefficient of 2. Power rule of logarithm: log_b(a^n) = n * log_b(a) 2log_4(2) = log_4(2^2)Rewrite Equation: Now, we rewrite the equation using the result from the power rule. log_4(3x) - log_4(2^2) = 2 log_4(3x) - log_4(4) = 2Combine Logarithmic Terms: Next, we apply the quotient rule of logarithms to combine the logarithmic terms on the left side. Quotient rule of logarithm: log_b(a) - log_b(c) = log_b(a/c) log_4(3x/4) = 2Convert to Exponential Form: To solve for x, we need to rewrite the logarithmic equation in exponential form. 4^2 = 3x/4Solve for x: Now, we solve for x by multiplying both sides of the equation by 4 and then dividing by 3. 16 * 4 = 3x 64 = 3x x = 64/3

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Solve for the exact value of
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log_(4)(3x)-2log_(4)(2)=2
Answer:

Solve for the exact value of $x$ . $\newline$ $\log _{4}(3 x)-2 \log _{4}(2)=2$ $\newline$ Answer:

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Precalculus

Quotient property of logarithms

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Q. Solve for the exact value of

x

\newline

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

\newline

Answer:

Apply Power Rule: Let's start by applying the power rule of logarithms to the term with the coefficient of $2$ . $\newline$ Power rule of logarithm: $\log_b(a^n) = n \cdot \log_b(a)$ $\newline$ $2\log_4(2) = \log_4(2^2)$
Rewrite Equation: Now, we rewrite the equation using the result from the power rule. $\newline$ $\log_4(3x) - \log_4(2^2) = 2$ $\newline$ $\log_4(3x) - \log_4(4) = 2$
Combine Logarithmic Terms: Next, we apply the quotient rule of logarithms to combine the logarithmic terms on the left side. $\newline$ Quotient rule of logarithm: $\log_b(a) - \log_b(c) = \log_b\left(\frac{a}{c}\right)$ $\newline$ $\log_4\left(\frac{3x}{4}\right) = 2$
Convert to Exponential Form: To solve for $x$ , we need to rewrite the logarithmic equation in exponential form. $4^2 = \frac{3x}{4}$
Solve for x: Now, we solve for $x$ by multiplying both sides of the equation by $4$ and then dividing by $3$ . $16 \times 4 = 3x$ $64 = 3x$ $x = \frac{64}{3}$