Solve for the exact value of x. log_(2)(9x)-log_(2)(2)=5 Answer:

Apply Quotient Rule: Apply the quotient rule of logarithms to combine the two logarithmic expressions into one. Quotient rule of logarithm: log₂(a) - log₂(b) = log₂(a/b) log₂(9x) - log₂(2) = log₂(9x/2)Use Logarithm Property: Rewrite the equation using the property of logarithms that states if log₂(a) = b, then 2^b = a. log₂(9x/2) = 5 implies 2^5 = 9x/2Calculate and Solve: Calculate 2^5 and solve for x. 2^5 = 32, so 32 = 9x/2Isolate 9x: Multiply both sides of the equation by 2 to isolate 9x on one side. 2 * 32 = 9x 64 = 9xDivide by 9: Divide both sides of the equation by 9 to solve for x. x = 64/9

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Solve for the exact value of
x.

log_(2)(9x)-log_(2)(2)=5
Answer:

Solve for the exact value of $x$ . $\newline$ $\log _{2}(9 x)-\log _{2}(2)=5$ $\newline$ Answer:

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Precalculus

Quotient property of logarithms

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Q. Solve for the exact value of

x

\newline

\log _{2}(9 x)-\log _{2}(2)=5

\newline

Answer:

Apply Quotient Rule: Apply the quotient rule of logarithms to combine the two logarithmic expressions into one. $\newline$ Quotient rule of logarithm: $\log_2(a) - \log_2(b) = \log_2\left(\frac{a}{b}\right)$ $\newline$ $\log_2(9x) - \log_2(2) = \log_2\left(\frac{9x}{2}\right)$
Use Logarithm Property: Rewrite the equation using the property of logarithms that states if $\log_2(a) = b$ , then $2^b = a$ . $\log_2(\frac{9x}{2}) = 5$ implies $2^5 = \frac{9x}{2}$
Calculate and Solve: Calculate $2^5$ and solve for $x$ . $\newline$ $2^5 = 32$ , so $32 = \frac{9x}{2}$
Isolate $9x$ : Multiply both sides of the equation by $2$ to isolate $9x$ on one side. $\newline$ $2 \times 32 = 9x$ $\newline$ $64 = 9x$
Divide by $9$ : Divide both sides of the equation by $9$ to solve for $x$ . $x = \frac{64}{9}$