Question

pls solve this
I will be greatful​

Answer 1

Answer:

1

Step-by-step explanation:

Need to know:

• log ₐ b = log b / log a, where the logs on RHS can be any base
• log ab = log a + log b

Then

$\displaystyle\frac1{\log_abc+1}+\frac1{\log_bca+1}+\frac1{\log_cab+1}\\\\=\frac1{\frac{\log bc}{\log a}+1}+\frac1{\frac{\log ca}{\log b}+1}+\frac1{\frac{\log ab}{\log c}+1}\\\\=\frac{\log a}{\log bc+\log a}+\frac{\log b}{\log ca+\log b}+\frac{\log c}{\log ab+\log c}\\\\=\frac{\log a}{\log b+\log c+\log a}+\frac{\log b}{\log c+\log a+\log b}+\frac{\log c}{\log a+\log b+\log c}\\\\=\frac{\log a+\log b+\log c}{\log a+\log b+\log c}\\\\=1$