Solve for the exact value of x. log_(6)(5x)-3log_(6)(5)=1 Answer:

Question

Solve for the exact value of  x.  log_(6)(5x)-3log_(6)(5)=1 Answer:

Bytelearn · Accepted Answer

Apply Power Rule: Apply the power rule of logarithms to simplify the term with the coefficient. The power rule states that a*log_b(c) = log_b(c^a), where a is a coefficient, b is the base of the logarithm, and c is the argument of the logarithm. In this case, we can rewrite 3log_(6)(5) as log_(6)(5^3). log_(6)(5x) - log_(6)(5^3) = 1Combine Logarithmic Terms: Use the property of logarithms that allows us to combine the two logarithmic terms into a single term by division. log_b(a) - log_b(c) = log_b(a/c), where b is the base of the logarithm, a and c are the arguments of the logarithms. We apply this property to combine the two terms. log_(6)(5x/5^3) = 1Simplify Argument: Simplify the argument of the logarithm. 5x/5^3 simplifies to x/5^2, since 5x divided by 5^3 is the same as 5x * 5^(-3), which simplifies to x/5^2. log_(6)(x/25) = 1Convert to Exponential: Convert the logarithmic equation to an exponential equation. If log_b(a) = c, then b^c = a. We apply this property to solve for x. 6^1 = x/25Solve for x: Solve for x by multiplying both sides of the equation by 25. x = 6 * 25 x = 150

Solve for the exact value of $x$ . $\newline$ $\log _{6}(5 x)-3 \log _{6}(5)=1$ $\newline$ Answer:

Full solution

More problems from Find derivatives of logarithmic functions

Related topics

Solve for the exact value of x x x.\newlinelog⁡6(5x)−3log⁡6(5)=1 \log _{6}(5 x)-3 \log _{6}(5)=1 log6​(5x)−3log6​(5)=1\newlineAnswer:

Solve for the exact value of $x$ . $\newline$ $\log _{6}(5 x)-3 \log _{6}(5)=1$ $\newline$ Answer: