Solve for the exact value of x. log_(3)(9x)-2log_(3)(3)=2 Answer:

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Solve for the exact value of  x.  log_(3)(9x)-2log_(3)(3)=2 Answer:

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Understand Logarithm Properties: Understand the properties of logarithms that can be used to simplify the equation. We can use the power rule of logarithms, which states that log_b(a^c) = c*log_b(a), to simplify the second term on the left side of the equation.Apply Power Rule: Apply the power rule to the second term of the equation. 2log_(3)(3) becomes log_(3)(3^2), since we can move the 2 in front of the log to the exponent of the argument.Simplify Using Logarithmic Properties: Simplify the equation using the fact that 3^2 is 9. log_(3)(9x) - log_(3)(9) = 2Combine Logarithmic Terms: Combine the logarithmic terms on the left side using the quotient rule of logarithms. The quotient rule states that log_b(a) - log_b(c) = log_b(a/c). Therefore, we can combine the two logarithms on the left into a single logarithm. log_(3)(9x/9) = 2Simplify Fraction Inside Logarithm: Simplify the fraction inside the logarithm. 9x/9 simplifies to x. log_(3)(x) = 2Convert to Exponential Equation: Convert the logarithmic equation to an exponential equation. Using the definition of a logarithm, log_b(a) = c is equivalent to b^c = a, we can rewrite the equation as: 3^2 = xCalculate Final Value: Calculate the value of 3^2. 3^2 is 9. x = 9

Solve for the exact value of $x$ . $\newline$ $\log _{3}(9 x)-2 \log _{3}(3)=2$ $\newline$ Answer:

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Solve for the exact value of x x x.\newlinelog⁡3(9x)−2log⁡3(3)=2 \log _{3}(9 x)-2 \log _{3}(3)=2 log3​(9x)−2log3​(3)=2\newlineAnswer:

Solve for the exact value of $x$ . $\newline$ $\log _{3}(9 x)-2 \log _{3}(3)=2$ $\newline$ Answer: