Find $\log_{p}X^2$?

Question

Given that $\log_{p}X=5$ and $\log_{p}Y=2$, find

i) $\log_{p}X^2$

I did this, $X=p^5$ and $Y=p^2$

But how do I use them? Should I find $p$?

Please people vote the answers so that I can choose the right answer cause everybody's right!! :D — Kiara, Jun 10 '14 at 14:35

score 4 · Accepted Answer · answered Jun 10 '14 at 14:33

4

Hint:
Just use the identity:

$$\log_{\,b}x^n=n\log_{\,b}x .$$

answered Jun 10 '14 at 14:33

Hakim

10,213

1

Better a good hint than the whole solution. +1 – DonAntonio Jun 10 '14 at 14:34
1

Thanks @DonAntonio ! $\overset{\cdot\cdot}\smile$ – Hakim Jun 10 '14 at 14:34
@حكيمالفيلسوفالضائع What about this? $log_{xy}P$? – Kiara Jun 10 '14 at 14:43
@Kiara What is $x,y$ and $P$? – Hakim Jun 10 '14 at 14:44
@حكيمالفيلسوفالضائع you mean the values? – Kiara Jun 10 '14 at 14:45
@Kiara No, what informations you were given about them. – Hakim Jun 10 '14 at 14:45
It's the same question...@حكيمالفيلسوفالضائع after that question I asked before, there was another one, $log_{p}\frac{1}{X}$ I solved that and found $-5$ and the next question is this. No other informations are included. – Kiara Jun 10 '14 at 14:47
@Kiara So since $\log_pX=5$ and $\log_pY=2$ we have $p^{\log_pX}=X=p^5$ and similarly $p^{\log_pY}=Y=p^2.$ Therefore $XY=p^{5}\cdot p^2=p^{7}.$ Can you take it from here? – Hakim Jun 10 '14 at 14:50
@حكيمالفيلسوفالضائع yeah thanks...I guess I got it! – Kiara Jun 10 '14 at 14:50
@حكيمالفيلسوفالضائع But you know this is like $log_{p^7}P$ how is this simplified because there is a power in the base? – Kiara Jun 10 '14 at 14:53
1

@Kiara Use the identity: $\log_{,b} x=\dfrac{\log_{,d} x}{\log_{,d} b}.$ – Hakim Jun 10 '14 at 14:56
@حكيمالفيلسوفالضائع okay, thanks a lot! :) – Kiara Jun 10 '14 at 14:56
1

@Kiara You're welcome, glad I could help! $\overset{\cdot\cdot}\smile$ – Hakim Jun 10 '14 at 14:57
1

@حكيمالفيلسوفالضائع um gonna give you a bounty :) – Kiara Jun 10 '14 at 14:59
1

@Kiara I'm the one who should give you a bounty ;-) – Hakim Jun 10 '14 at 15:01
@حكيمالفيلسوفالضائع hahaha why is that? – Kiara Jun 10 '14 at 15:01
1

@Kiara You deserve it, don't you? ;-) – Hakim Jun 10 '14 at 15:03
@حكيمالفيلسوفالضائع you deserve it! You help people, solving maths ain't easy! But you still help us :D :') – Kiara Jun 10 '14 at 15:04

score 2 · Answer 2 · answered Jun 10 '14 at 14:33

2

$\log_p X^2 = 2 \log_p X = 2 \cdot 5 = 10$.

answered Jun 10 '14 at 14:33

Eric Towers

67,037

score 2 · Answer 3 · answered Jun 10 '14 at 14:33

2

$log_pX^2=log_p(p^5)^2=log_p(p^{10})=10$

answered Jun 10 '14 at 14:33

RE60K

17,716

Find $\log_{p}X^2$?

3 Answers3