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Let log,4=3; log,C=2; log, D=5
What is the value of Logb A^3D^4/C^2 ?

Let log,4=3; log,C=2; log, D=5 What is the value of Logb A^3D^4/C^2 ?-example-1

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6 votes

Answer:

D. 25

Explanation:

To find the value of the given logarithmic expression, first rewrite the expression use log laws.


\boxed{\begin{minipage}{7cm}\underline{Log Laws}\\\\Product law: \quad $\log_axy=\log_ax + \log_ay$\\\\Power law: $\quad\;\;\: \log_ax^n=n\log_ax$\\\\Quotient law:\quad$\log_a \left((x)/(y)\right)=\log_ax - \log_ay$\\\end{minipage}}

Apply the quotient law, followed by the product law, and finally the power law:


\begin{aligned}\implies \log_b(A^3D^4)/(C^2) &=\log_b A^3D^4 - \log_b C^2\\& =\log_b A^3+ \log_bD^4 - \log_b C^2\\& =3\log_b A+ 4\log_bD - 2\log_b C\end{aligned}

Given:


  • \log_bA=3

  • \log_bC=2

  • \log_bD=5

Substitute the given values into the rewritten expression:


\begin{aligned}\implies \log_b(A^3D^4)/(C^2) &=3\log_b A+ 4\log_bD - 2\log_b C\\&=3(3)+ 4(5) - 2(2)\\&=9+20-4\\&=29-4\\&=25\end{aligned}

Therefore, the value of the logarithmic expression is 25.

User BBonDoo
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