Solve for the exact value of x. log_(4)(8x)-log_(4)(8)=3 Answer:

Combine logarithms: Apply the quotient rule of logarithms to combine the two logarithms into one. Quotient rule of logarithms: log_b(a) - log_b(c) = log_b(a/c) log_4(8x) - log_4(8) = log_4(8x/8) Simplify the fraction inside the logarithm. log_4(8x/8) = log_4(x)Simplify fraction: Set the combined logarithm equal to 3. log_4(x) = 3 Now, we need to rewrite this logarithmic equation in exponential form. 4^3 = x Calculate the value of 4^3. 4^3 = 64Set equal to 3: Solve for x. x = 64

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Solve for the exact value of
x.

log_(4)(8x)-log_(4)(8)=3
Answer:

Solve for the exact value of $x$ . $\newline$ $\log _{4}(8 x)-\log _{4}(8)=3$ $\newline$ Answer:

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Precalculus

Quotient property of logarithms

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Q. Solve for the exact value of

x

\newline

\log _{4}(8 x)-\log _{4}(8)=3

\newline

Answer:

Combine logarithms: Apply the quotient rule of logarithms to combine the two logarithms into one. $\newline$ Quotient rule of logarithms: $\log_b(a) - \log_b(c) = \log_b\left(\frac{a}{c}\right)$ $\newline$ $\log_4(8x) - \log_4(8) = \log_4\left(\frac{8x}{8}\right)$ $\newline$ Simplify the fraction inside the logarithm. $\newline$ $\log_4\left(\frac{8x}{8}\right) = \log_4(x)$
Simplify fraction: Set the combined logarithm equal to $3$ . $\newline$ $\log_4(x) = 3$ $\newline$ Now, we need to rewrite this logarithmic equation in exponential form. $\newline$ $4^3 = x$ $\newline$ Calculate the value of $4^3$ . $\newline$ $4^3 = 64$
Set equal to $3$ : Solve for $x$ . $x = 64$