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Find the numerical value of the log expression. {:[log a=-4quad log b=-5quad log c=-9],[log ((c^(9))/(a^(3)b^(8)))]:} Answer:

Find the numerical value of the log expression.\newlinelog⁡a=−4log⁡b=−5log⁡c=−9log⁡c9a3b8 \begin{array}{c} \log a=-4 \quad \log b=-5 \quad \log c=-9 \\ \log \frac{c^{9}}{a^{3} b^{8}} \end{array} \newlineAnswer:

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Q. Find the numerical value of the log expression.\newlinelog⁡a=−4log⁡b=−5log⁡c=−9log⁡c9a3b8 \begin{array}{c} \log a=-4 \quad \log b=-5 \quad \log c=-9 \\ \log \frac{c^{9}}{a^{3} b^{8}} \end{array} \newlineAnswer:
  1. Given Logarithms: We are given the logarithms of aa, bb, and cc as log⁡a=−4\log a = -4, log⁡b=−5\log b = -5, and log⁡c=−9\log c = -9. We need to find the value of log⁡(c9a3b8)\log\left(\frac{c^{9}}{a^{3}b^{8}}\right).\newlineUsing the properties of logarithms, we can express the logarithm of a quotient as the difference of logarithms. We can also bring the exponents in front of the logarithms.
  2. Apply Logarithm Properties: Apply the properties of logarithms to the expression log⁡(c9a3b8)\log\left(\frac{c^{9}}{a^{3}b^{8}}\right).log⁡(c9a3b8)=9log⁡(c)−3log⁡(a)−8log⁡(b)\log\left(\frac{c^{9}}{a^{3}b^{8}}\right) = 9\log(c) - 3\log(a) - 8\log(b)
  3. Substitute Values: Substitute the given values of log⁡a\log a, log⁡b\log b, and log⁡c\log c into the expression.9⋅log⁡(c)−3⋅log⁡(a)−8⋅log⁡(b)=9⋅(−9)−3⋅(−4)−8⋅(−5)9\cdot\log(c) - 3\cdot\log(a) - 8\cdot\log(b) = 9\cdot(-9) - 3\cdot(-4) - 8\cdot(-5)
  4. Perform Arithmetic Operations: Perform the arithmetic operations. 9∗(−9)−3∗(−4)−8∗(−5)=−81+12+409*(-9) - 3*(-4) - 8*(-5) = -81 + 12 + 40
  5. Complete Calculation: Complete the calculation to find the numerical value. −81+12+40=−81+52=−29-81 + 12 + 40 = -81 + 52 = -29

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