Question

log sub a5=.699 and log sub a 3=.477. Use these values to evaluate log sub a 45.

Answer 1

Is this your question?

\( \log_a 5 = 0.699\)
\( \log_a 3 = 0.477\)
Find \(\log_a 45\)

Answer 2

yes

Answer 3

Remember these two important rules of logs:

\(\log_a x^m = m \log_a x \)
\( \log_a (xy) = \log_a x + \log_a y\)

Answer 4

Can you break down 45 into the product of its prime factors?

Answer 5

how were you able to type the sub a?

Answer 6

I'm using the equation editor.

Answer 7

I came up with 1.653 as my answer but not sure if it's right. i did 2(.477) +.699

Answer 8

because 3^2 * 5 would equal 45

Answer 9

That's it.
Here's how you do it.

\(45 = 3^2 \cdot 5\)

\(\log_a 45\)

\( = \log_a (3^2 \cdot 5)\)

\( = \log_a 3^2 + \log_a 5 \)

\(= 2 \log_a 3 + \log_a 5\)

\(= 2 \cdot 0.477 + 0.699\)

Answer 10

Which is what you did.
Great job!

Answer 11

thank you so much!

Answer 12

You're very welcome.