Question

Which is the correct letter answer of the value of the log equation?

Answer 1

Answer:

The value of the single logarithm is -11 ⇒ answer B

Step-by-step explanation:

* Lets revise the rule of the logarithmic functions

# ㏒ a + ㏒ b = ㏒ ab  

# ㏒ a - ㏒ b = ㏒ a/b

# ㏒ a^n = n ㏒ a  

# ㏒ 1 = 0  

* Now lets solve the problem

∵ $log_{b}(\frac{A^{5}C^{2}}{D^{6}})$

- Change the single logarithm to an expression by change the

  multiplication to addition and the division to subtraction

∵ $log_{b}A^{5}=5log_{b}A$

∵ $log_{b}C^{2}=2log_{b}C$

∵ $log_{b}D^{6}=6log_{b}D$

∴ The single logarithm = $5log_{b}A+2log_{b}C-6log_{b}D$

* Now lets substitute the values

∵ $log_{b}A=3;===log_{b}C=2;===log_{b}D=5$

- Substitute the values into the expression

∴ The value = 5(3) + 2(2) - 6(5) = 15 + 4 - 30 = -11

* The value of the single logarithm is -11