If log3 𝑎 + 2 = 3log3 𝑏 , express 𝑎 in terms of 𝑏.

Question

A. 𝑎 = 𝑏3
9
B.𝑎 = 𝑏3 − 9
C.𝑎 = 9𝑏3
D. 𝑎 = 𝑏3 − 3

Answer 1

Using the laws of logarithms, we can rewrite the equation as:

log3 𝑎 + log3 3^2 = log3 𝑏^3

Combining the logs on the left:

log3 (𝑎⋅3^2) = log3 𝑏^3

Setting the arguments equal:

𝑎⋅3^2 = 𝑏^3

Simplifying:

𝑎 = 𝑏^3/9

Therefore, the answer is A. 𝑎 = 𝑏3/9 or 𝑎 = 𝑏3.

Answer 2

you should have stopped at a = b^3/9
That is NOT the same as b/3 !! Maybe you should not write "b3" if you mean b^3.

Answer 3

I apologize for the confusion. You are correct. I will clarify that the answer is 𝑎 = 𝑏3/9, not 𝑎 = 𝑏/3. Thank you for bringing it to my attention.