Question

Solve.
Let logbA=2.627 and logbB=0.348. Find logb AB

Answer 1

This is one of your log rules.

Answer 2

\[\log_{b} (x) + \log_{b} (y) = \log_{b} (xy) \]

Answer 3

So it's 2.975

Answer 4

Hard to say without knowing b.

Answer 5

ok

Answer 6

I'm not saying you should give up on it. Just asking if you solved for b.

Answer 7

You know:

\(\log_{b} (A) + \log_{b} (B) = \log_{b} (AB)\)
\(\log_{b} (A) = 2.627\)
\(\log_{b} (B) = 0.348\)

So:

\(2.627 + 0.348 = \log_{b} (2.627 \times 0.348)\)

Answer 8

\(2.975 = \log_{b}(.9142)\)

\(2.975 = \frac{\log_{10} (.9142)}{\log_{10} (b)}\)

\(\log b = \frac{-0.089706}{2.975} = -0.03015\)

\(b = 10^{-0.03015} = 0.932925\)

Knowing that, you can solve \(\log_{b} (AB)\)