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he exact value of x. log_(5)(3x)+3log_(5)(2)=3 I Attempt 2 out of 2

he exact value of x x .\newlinelog⁡5(3x)+3log⁡5(2)=3 \log _{5}(3 x)+3 \log _{5}(2)=3 \newlineI Attempt 22 out of 22

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Find derivatives of logarithmic functionsright chevron icon

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Q. he exact value of x x .\newlinelog⁡5(3x)+3log⁡5(2)=3 \log _{5}(3 x)+3 \log _{5}(2)=3 \newlineI Attempt 22 out of 22
  1. Apply Power Rule: Use the power rule for logarithms to simplify the second term.\newline3log⁡5(2)=log⁡5(23)3\log_5(2) = \log_5(2^3)
  2. Rewrite Equation: Rewrite the equation using the simplified second term. log⁡5(3x)+log⁡5(8)=3\log_5(3x) + \log_5(8) = 3
  3. Combine Logarithms: Combine the logarithms on the left side using the product rule for logarithms. log⁡5(3x⋅8)=3\log_5(3x \cdot 8) = 3
  4. Simplify Product: Simplify the product inside the logarithm. log⁡5(24x)=3\log_5(24x) = 3
  5. Convert to Exponential Form: Convert the logarithmic equation to its exponential form.\newline53=24x5^3 = 24x
  6. Calculate Value: Calculate 535^3 to find the value of 24x24x.\newline125=24x125 = 24x
  7. Divide to Solve: Divide both sides by 2424 to solve for xx.\newlinex=12524x = \frac{125}{24}
  8. Find Exact Value: Perform the division to find the exact value of xx.x=5.208333…x = 5.208333\ldots

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