I am ask to express logarithms in terms of a and b

Question

Here the question,I have try to obtain the answer. My answer is $2a+2b-2$, but I not sure with my answer

Given $\log_x2=a$ and $\log_x 3=b$, write $\log_x\dfrac{4}{9x^2}$ in terms of $a$ and $b$

Your answer is correct. – José Carlos Santos Apr 13 '20 at 11:02 — José Carlos Santos, Apr 13 '20 at 11:02
@JoséCarlosSantos it should be $2a-2b-2$ – Qurultay Apr 13 '20 at 11:04 — Qurultay, Apr 13 '20 at 11:04
@Qurultay Sure! My bad. – José Carlos Santos Apr 13 '20 at 11:09 — José Carlos Santos, Apr 13 '20 at 11:09
@JinHaoFoo then you did correct. – Qurultay Apr 13 '20 at 11:11 — Qurultay, Apr 13 '20 at 11:11

score 1 · Answer 1 · answered Apr 13 '20 at 11:03

1

You did a sign mistake. Note $$\log_x\frac{4}{9x^2}=\log_x 4-\log_x(9x^2)\\ =2\log_x 2-(\log_x 9+\log_x x^2)\\= 2a-(2b+2)\\=2a-2b-2$$

answered Apr 13 '20 at 11:03

Qurultay

score 0 · Answer 2 · answered Apr 13 '20 at 11:03

$\log_x(2) = a, \log_x(3)=b$. Then

$$\log_x(\frac{4}{9x^2}) = \log_x(4) - \log_x(9x^2) = \log_x(2^2) - \left(\log_x(3^2) + \log_x(x^2)\right)\\ = 2\log_x(2)-2\log_x(3) - 2$$

So we get $2a-2b-2$ after using the definitions of $a$ and $b$. By definition $\log_x(x^2)=2$ of course.

score 0 · Answer 3 · answered Apr 13 '20 at 11:06

0

$$N=\log_x\frac{4}{9x^2}=\log_x 4-\log_x 9-\log_x x^2=2\log_x 2-2 \log_x 3-2=2a-2b-2$$

answered Apr 13 '20 at 11:06

Z Ahmed

3 Answers3