Logs question

I know this question can be answered in an easier way, but it should be possible to reach the correct answer using my method as shown. Please can you tell me what I have done wrong? I am correct that (3^x)(5^x) = 15^2x aren't I?
ImageUploadedByStudent Room1443965026.443809.jpg

ImageUploadedByStudent Room1443965026.443809.jpg

Posted from TSR Mobile

Reply 1

r3l3ntl3ss

3^x * 5^x is not the same as 15^(2x). Suppose x is 1: 3 * 5 doesn't equal 15^2.

On your third step take xlog3(5) to the RHS and the rest should be clear.

Should be 15^x.

Original post by Matureb

Should be 15^x.

I don't understand why this is. According to laws of indices a^m(b^n) = ab^m+n

Posted from TSR Mobile

Reply 4

davros

Original post by anoymous1111

I don't understand why this is. According to laws of indices a^m(b^n) = ab^m+n

Posted from TSR Mobile

Where've you got that from? That's not a law of indices!

Imagine you were starting from the other end:

15^a = (3 \times 5)^a = 3^a \times 5^a

by the correct law of indices :smile:

Reply 5

anoymous1111

Original post by davros

Where've you got that from? That's not a law of indices!

Imagine you were starting from the other end:

15^a = (3 \times 5)^a = 3^a \times 5^a

by the correct law of indices :smile:

Oooooh ok. Lol guess I got it wrong!

Posted from TSR Mobile

Reply 6

anoymous1111

Original post by davros

Where've you got that from? That's not a law of indices!

Imagine you were starting from the other end:

15^a = (3 \times 5)^a = 3^a \times 5^a

by the correct law of indices :smile:

But it does say this on many websites: ImageUploadedByStudent Room1443967646.472040.jpg

I don't see why it's wrong

Posted from TSR Mobile

Reply 7

davros

Original post by anoymous1111

But it does say this on many websites: ImageUploadedByStudent Room1443967646.472040.jpg

I don't see why it's wrong

Posted from TSR Mobile

That law is correct - both numbers have the same base a so when you multiply them you can just add the exponents!

If you have numbers with 2 different bases like a and b then you can't do anything to simplify the product - unless the exponents are the same too.

So:

a^m \times b^n

can't be simplified - bases and exponents are both different.

But

a^m \times b^m = (ab)^m

- different bases but same exponent.

Reply 8

anoymous1111

Original post by davros

a^m \times b^n

can't be simplified - bases and exponents are both different.

But

a^m \times b^m = (ab)^m

- different bases but same exponent.

Ooooooooh hahaaa thank you so much!

Posted from TSR Mobile

Reply 9

anoymous1111

Original post by Dabo_26

I feel like you are overcomplicating things,

3^x = 5^(1-x)
xlog3 = (1-x)log5 (taking logs)
xlog3=log5 - xlog5 (expand brackets)
xlog3+xlog5=log5 (collect x terms)
x(log3+log5)=log5 (factorise)
therefore
x = (log5) / log3 + log 5
= 0.594

Thank you!

Posted from TSR Mobile

Reply 10

Louisb19

Original post by anoymous1111

Posted from TSR Mobile

Half of your working is pointless, in the first half you use logs to show that 3^x = 5^(1-x) is the same as as 3^x = (5)/(5^x) which you can just see from the indices, no need to spend so long working it out. Also you can't multiply like that which is why you got the wrong answer in the end. 3^x * 5^x =/ 15^2x .

Reply 11

Zacken

Original post by Dabo_26

I feel like you are overcomplicating things,

Full solutions are against the rules of this forum.

Reply 12

davros

Original post by Dabo_26

I feel like you are overcomplicating things,

Please don't post full solutions - it's against forum guidelines :smile:

Reply 13

Dabo_26

Original post by Zacken

Full solutions are against the rules of this forum.

whoops sorry! deleted post :-p

Reply 14

Zacken

Original post by Dabo_26

whoops sorry! deleted post :-p

It's a little too late now, but you know for next time, you didn't need to delete your post wither, just edit it to make it more of a hints than an answer.

Thank you, though! :smile: