Find the numerical value of the log expression. {:[log a=10quad log b=7quad log c=-6],[log ((sqrtc)/(a^(4)b^(5)))]:} Answer:

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Find the numerical value of the log expression.  {:[log a=10quad log b=7quad log c=-6],[log ((sqrtc)/(a^(4)b^(5)))]:} Answer:

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Apply Quotient Rule: Let's start by expressing the given logarithm using the properties of logarithms. We have the expression log((sqrt(c))/(a^(4)b^(5))). Using the quotient rule of logarithms, which states that log(a/b) = log(a) - log(b), we can separate the numerator and the denominator.Expand Numerator and Denominator: Now, we apply the quotient rule to the given expression: log((sqrt(c))/(a^(4)b^(5))) = log(sqrt(c)) - log(a^(4)b^(5)).Simplify Using Rules: Next, we use the product rule of logarithms for the denominator, which states that log(a*b) = log(a) + log(b), and the power rule, which states that log(a^n) = n*log(a), to further expand the expression: log(sqrt(c)) - (log(a^(4)) + log(b^(5))).Apply Power Rule: We can simplify the expression by applying the power rule to the terms log(a^(4)) and log(b^(5)), and recognizing that sqrt(c) is c^(1/2): log(c^(1/2)) - (4*log(a) + 5*log(b)).Substitute Given Values: Now we apply the power rule to log(c^(1/2)), which gives us (1/2)*log(c): (1/2)*log(c) - (4*log(a) + 5*log(b)).Perform Arithmetic Operations: We substitute the given values for log(a), log(b), and log(c) into the expression: (1/2)*(-6) - (4*10 + 5*7).Combine Terms and Subtract: Perform the arithmetic operations: -3 - (40 + 35).Get Numerical Value: Combine the terms inside the parentheses and then subtract from -3: -3 - 75.Finally, we get the numerical value of the expression: -3 - 75 = -78.

Find the numerical value of the log expression. $\newline$ $\begin{array}{c} \log a=10 \quad \log b=7 \quad \log c=-6 \\ \log \frac{\sqrt{c}}{a^{4} b^{5}} \end{array}$ $\newline$ Answer:

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Find the numerical value of the log expression.\newlinelog⁡a=10log⁡b=7log⁡c=−6log⁡ca4b5 \begin{array}{c} \log a=10 \quad \log b=7 \quad \log c=-6 \\ \log \frac{\sqrt{c}}{a^{4} b^{5}} \end{array} loga=10logb=7logc=−6loga4b5c​​​\newlineAnswer:

Find the numerical value of the log expression. $\newline$ $\begin{array}{c} \log a=10 \quad \log b=7 \quad \log c=-6 \\ \log \frac{\sqrt{c}}{a^{4} b^{5}} \end{array}$ $\newline$ Answer: