Find the numerical value of the log expression. {:[log a=9quad log b=6quad log c=4],[log ((sqrt(b^(5)c^(5)))/(a^(9)))]:} Answer:

Question

Find the numerical value of the log expression.  {:[log a=9quad log b=6quad log c=4],[log ((sqrt(b^(5)c^(5)))/(a^(9)))]:} Answer:

Bytelearn · Accepted Answer

Identify Given Logarithm Values: Identify the given logarithm values and the expression to evaluate. We are given that log a = 9, log b = 6, and log c = 4. We need to find the numerical value of log ((sqrt(b^(5)c^(5)))/(a^(9))).Apply Logarithm Properties: Apply the properties of logarithms to simplify the expression. First, we use the quotient rule of logarithms, which states that log(a/b) = log(a) - log(b). log ((sqrt(b^(5)c^(5)))/(a^(9))) = log (sqrt(b^(5)c^(5))) - log (a^(9))Simplify Square Root: Simplify the square root and apply the power rule of logarithms. The power rule of logarithms states that log(a^k) = k * log(a). The square root is equivalent to raising to the power of 1/2. log (sqrt(b^(5)c^(5))) = log ((b^(5)c^(5))^(1/2)) = (1/2) * log (b^(5)c^(5))Apply Product Rule: Apply the product rule of logarithms to the term inside the square root. The product rule of logarithms states that log(a * b) = log(a) + log(b). (1/2) * log (b^(5)c^(5)) = (1/2) * (log (b^(5)) + log (c^(5)))Apply Power Rule: Apply the power rule to the logarithms of b and c. log (b^(5)) = 5 * log (b) and log (c^(5)) = 5 * log (c). (1/2) * (log (b^(5)) + log (c^(5))) = (1/2) * (5 * log (b) + 5 * log (c))Substitute Given Values: Substitute the given values of log b and log c into the expression. log b = 6 and log c = 4, so we substitute these values in. (1/2) * (5 * log (b) + 5 * log (c)) = (1/2) * (5 * 6 + 5 * 4)Perform Arithmetic Operations: Perform the arithmetic operations. (1/2) * (5 * 6 + 5 * 4) = (1/2) * (30 + 20) = (1/2) * 50 = 25Apply Power Rule to Logarithm: Apply the power rule to the logarithm of a^(9). log (a^(9)) = 9 * log (a) and substitute the given value of log a = 9. log (a^(9)) = 9 * 9 = 81Combine Results: Combine the results to find the final value of the original expression. log ((sqrt(b^(5)c^(5)))/(a^(9))) = 25 - 81Perform Final Subtraction: Perform the final subtraction to get the numerical value. 25 - 81 = -56

Find the numerical value of the log expression. $\newline$ $\begin{array}{c} \log a=9 \quad \log b=6 \quad \log c=4 \\ \log \frac{\sqrt{b^{5} c^{5}}}{a^{9}} \end{array}$ $\newline$ Answer:

Full solution

More problems from Quotient property of logarithms

Related topics

Find the numerical value of the log expression.\newlinelog⁡a=9log⁡b=6log⁡c=4log⁡b5c5a9 \begin{array}{c} \log a=9 \quad \log b=6 \quad \log c=4 \\ \log \frac{\sqrt{b^{5} c^{5}}}{a^{9}} \end{array} loga=9logb=6logc=4loga9b5c5​​​\newlineAnswer:

Find the numerical value of the log expression. $\newline$ $\begin{array}{c} \log a=9 \quad \log b=6 \quad \log c=4 \\ \log \frac{\sqrt{b^{5} c^{5}}}{a^{9}} \end{array}$ $\newline$ Answer: