Solve for the exact value of x. log_(6)(4x)+log_(6)(9)=3 Answer:

Apply product rule of logarithms: Apply the product rule of logarithms to combine the two logarithmic terms. The product rule of logarithms states that log_b(m) + log_b(n) = log_b(m*n). Therefore, log_6(4x) + log_6(9) becomes log_6(4x * 9).Simplify expression: Simplify the expression inside the logarithm. Multiplying 4x by 9 gives us 36x. So, log_6(4x * 9) simplifies to log_6(36x).Set equal to 3: Set the simplified logarithmic expression equal to 3. We now have the equation log_6(36x) = 3.Convert to exponential form: Convert the logarithmic equation to its exponential form. The exponential form of log_b(a) = c is b^c = a. So, 6^3 = 36x.Calculate value of 6^3: Calculate the value of 6^3. 6^3 equals 216. So, we have 216 = 36x.Solve for x: Solve for x by dividing both sides of the equation by 36. Dividing 216 by 36 gives us x = 216 / 36.Calculate exact value of x: Calculate the exact value of x. 216 divided by 36 equals 6. So, x = 6.

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Solve for the exact value of
x.

log_(6)(4x)+log_(6)(9)=3
Answer:

Solve for the exact value of $x$ . $\newline$ $\log _{6}(4 x)+\log _{6}(9)=3$ $\newline$ Answer:

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Precalculus

Quotient property of logarithms

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Q. Solve for the exact value of

x

\newline

\log _{6}(4 x)+\log _{6}(9)=3

\newline

Answer:

Apply product rule of logarithms: Apply the product rule of logarithms to combine the two logarithmic terms. $\newline$ The product rule of logarithms states that $\log_b(m) + \log_b(n) = \log_b(m*n)$ . $\newline$ Therefore, $\log_6(4x) + \log_6(9)$ becomes $\log_6(4x \cdot 9)$ .
Simplify expression: Simplify the expression inside the logarithm. $\newline$ Multiplying $4x$ by $9$ gives us $36x$ . $\newline$ So, $\log_6(4x \times 9)$ simplifies to $\log_6(36x)$ .
Set equal to $3$ : Set the simplified logarithmic expression equal to $3$ . We now have the equation $\log_6(36x) = 3$ .
Convert to exponential form: Convert the logarithmic equation to its exponential form. $\newline$ The exponential form of $\log_b(a) = c$ is $b^c = a$ . $\newline$ So, $6^3 = 36x$ .
Calculate value of $6^3$ : Calculate the value of $6^3$ . $\newline$ $6^3$ equals $216$ . $\newline$ So, we have $216 = 36x$ .
Solve for x: Solve for x by dividing both sides of the equation by $36$ . $\newline$ Dividing $216$ by $36$ gives us $x = \frac{216}{36}$ .
Calculate exact value of x: Calculate the exact value of $x$ . $216$ divided by $36$ equals $6$ . So, $x = 6$ .