Solve for the exact value of x. log_(6)(6x)+2log_(6)(4)=1 Answer:

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Solve for the exact value of  x.  log_(6)(6x)+2log_(6)(4)=1 Answer:

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Apply power rule: Apply the power rule of logarithms to the second term. The power rule states that log_b(a^c) = c * log_b(a). We can apply this to the second term 2log_(6)(4) to simplify the equation. log_(6)(6x) + log_(6)(4^2) = 1Simplify second logarithm: Simplify the second logarithm. 4^2 is 16, so we can rewrite the equation as: log_(6)(6x) + log_(6)(16) = 1Combine logarithms: Combine the logarithms on the left side using the product rule. The product rule states that log_b(m) + log_b(n) = log_b(m*n). We can combine the two logarithms into one. log_(6)(6x * 16) = 1Simplify product inside: Simplify the product inside the logarithm. 6x * 16 = 96x, so the equation becomes: log_(6)(96x) = 1Convert to exponential: Convert the logarithmic equation to an exponential equation. If log_b(a) = c, then b^c = a. We can apply this to our equation to solve for x. 6^1 = 96xSolve for x: Solve for x. Divide both sides by 96 to isolate x. x = 6 / 96Simplify the fraction: Simplify the fraction. 6 / 96 can be simplified by dividing both numerator and denominator by 6. x = 1 / 16

Solve for the exact value of $x$ . $\newline$ $\log _{6}(6 x)+2 \log _{6}(4)=1$ $\newline$ Answer:

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Solve for the exact value of x x x.\newlinelog⁡6(6x)+2log⁡6(4)=1 \log _{6}(6 x)+2 \log _{6}(4)=1 log6​(6x)+2log6​(4)=1\newlineAnswer:

Solve for the exact value of $x$ . $\newline$ $\log _{6}(6 x)+2 \log _{6}(4)=1$ $\newline$ Answer: