Question

I need help working through a couple logarithm equations. If someone could please help me.
1/2log6(25)+log6(x)=log6(20)
log2(4)-log2(x+3)=log2(8)

Answer 1

Is that first one 0.5log6(25) or 1/(2log625)?

Answer 2

0.5log6(25)+log6(x)=log6(20)

Answer 3

What log rules do you know?

Answer 4

Well my teacher gave us ways to solve them like loga(x)=loga(y), x=y and loga(x*y)=loga(x)+loga(y)
but he didn't talk about log rules.

Answer 5

Yep, those are two. Here's one more that you'll need:
\[a\log(x)=\log(x^a)\]

Answer 6

So for your first question:

1/2log6(25)+log6(x)=log6(20)

Before we can combine the left side into one using log(a)+log(b)=log(ab), we need to do something about that 0.5 at the start. Can you use the rule I just posted to change it?

Answer 7

so put the 0.5 as the exponent for log6(25) right?

Answer 8

Almost, it's only the exponent for for the 25. So it would go to \(\log_6(25^{0.5})\)

Answer 9

Can you simplify that?

Answer 10

Alright I have it like that on my paper and it would simplify to log6(5) am I correct?

Answer 11

Yep, that's correct. Now the next step:

log6(5)+log6(x)=log6(20)
log6(5x)=log6(20)

Can you tell me the answer? When you've done that, have a go at the second one and I'll check your working.

Answer 12

put the 5x=20 divide by 5 and get x=4
am i correct on that?

Answer 13

Yes that's correct. Really sorry but I've got to go. I've written up your solutions, but please try the question yourself and check your answer against mine when you've done it:

http://pastebin.com/heXsNeGA

Answer 14

Alright, and that is just fine. Thank you for all your help!

Answer 15

@bamber2017 can i help you to continue it ?

Answer 16

I actually think I figured it out. Thank you anyway.

Answer 17

np - ok -- good luck

bye