Algebra
Logarithms
MMTS_Full_Test_10
Grade 12
Question:
If $x=\log_a(bc)$, $y=\log_b(ca)$, $z=\log_c(ab)$, then $\dfrac{1}{x+1}+\dfrac{1}{y+1}+\dfrac{1}{z+1}=$
Step-by-Step Solution
Key Concept: $x+1=\log_a(bc)+\log_a a=\log_a(abc)$
$\frac{1}{x+1}+\frac{1}{y+1}+\frac{1}{z+1}=\log_{abc}a+\log_{abc}b+\log_{abc}c=\log_{abc}(abc)=1$.
Correct Answer: 1