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
∵ [tex]log_{b}(\frac{A^{5}C^{2}}{D^{6}})[/tex]
- Change the single logarithm to an expression by change the
multiplication to addition and the division to subtraction
∵ [tex]log_{b}A^{5}=5log_{b}A[/tex]
∵ [tex]log_{b}C^{2}=2log_{b}C[/tex]
∵ [tex]log_{b}D^{6}=6log_{b}D[/tex]
∴ The single logarithm = [tex]5log_{b}A+2log_{b}C-6log_{b}D[/tex]
* Now lets substitute the values
∵ [tex]log_{b}A=3;===log_{b}C=2;===log_{b}D=5[/tex]
- 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
