Find the numerical value of the log expression. {:[log a=9quad log b=2quad log c=-6],[log ((root(3)(c^(5)))/(a^(9)b^(4)))]:} Answer:

Question

Find the numerical value of the log expression.  {:[log a=9quad log b=2quad log c=-6],[log ((root(3)(c^(5)))/(a^(9)b^(4)))]:} Answer:

Bytelearn · Accepted Answer

Apply Quotient Rule: Let's start by expressing the given logarithm using the properties of logarithms. We have log ((root(3)(c^(5)))/(a^(9)b^(4))). First, we apply the quotient rule of logarithms, which states that log(a/b) = log(a) - log(b).Rewrite as Difference: Now we rewrite the expression as a difference of two logarithms: log(root(3)(c^(5))) - log(a^(9)b^(4)).Apply Power Rule: Next, we apply the power rule of logarithms, which states that log(a^n) = n*log(a), to the terms inside the logarithms. For the first term, since root(3)(c^(5)) is the same as c^(5/3), we get log(c^(5/3)) = (5/3)*log(c). For the second term, we have two variables inside the logarithm, so we apply the product rule of logarithms, log(a*b) = log(a) + log(b), before applying the power rule.Apply Product Rule: Applying the product rule to the second term gives us log(a^(9)) + log(b^(4)). Now we apply the power rule to each of these terms to get 9*log(a) and 4*log(b).Distribute Negative Sign: Our expression now looks like this: (5/3)*log(c) - (9*log(a) + 4*log(b)). We distribute the negative sign through the parenthesis to get: (5/3)*log(c) - 9*log(a) - 4*log(b).Substitute Given Values: Now we substitute the given values of log a, log b, and log c into the expression. This gives us (5/3)*(-6) - 9*9 - 4*2.Perform Arithmetic Operations: We perform the arithmetic operations: (5/3)*(-6) = -10, 9*9 = 81, and 4*2 = 8. So the expression simplifies to -10 - 81 - 8.Find Numerical Value: Finally, we add the numbers together to find the numerical value of the expression: -10 - 81 - 8 = -99.

Find the numerical value of the log expression. $\newline$ $\begin{array}{c} \log a=9 \quad \log b=2 \quad \log c=-6 \\ \log \frac{\sqrt[3]{c^{5}}}{a^{9} b^{4}} \end{array}$ $\newline$ Answer:

Full solution

More problems from Quotient property of logarithms

Related topics

Find the numerical value of the log expression.\newlinelog⁡a=9log⁡b=2log⁡c=−6log⁡c53a9b4 \begin{array}{c} \log a=9 \quad \log b=2 \quad \log c=-6 \\ \log \frac{\sqrt[3]{c^{5}}}{a^{9} b^{4}} \end{array} loga=9logb=2logc=−6loga9b43c5​​​\newlineAnswer:

Find the numerical value of the log expression. $\newline$ $\begin{array}{c} \log a=9 \quad \log b=2 \quad \log c=-6 \\ \log \frac{\sqrt[3]{c^{5}}}{a^{9} b^{4}} \end{array}$ $\newline$ Answer: