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# C2 logs wherre have i gone wrong? watch

1. 1. Write as a single Logarithm, then simplfy your answer

I have written the bases in the brackets, its obvious which ones they are.

2log(10)20- (log(10)5+log(10)8)

= log(10)400/ log(10) 40 = log(10) 40/log(10)4 = log(10)10/log(10)1

But the answer at the back is: log (10) 10=1

log(8)25 + log(8)10 - 3log(8)5 = log(8) 250/ log (8) 125

The answer at the back of the book is: log(8)2=1/3

Thank you very much!
2. 2log(10)20- (log(10)5+log(10)8)

= log(10)(400/40) = log(10) 10 = 1

log(8)25 + log(8)10 - 3log(8)5 = log(8) (250/125) = log(8)2=1/3

log(a) (b) + log(a)(c) = log(a)(bc)

log(a) (b) - log(a)(c) = log(a)(b/c)

Different to the rule

log(a)(b)/log(a)(c) = log(c)(b)
3. (Original post by LondonBoy)
1. Write as a single Logarithm, then simplfy your answer

I have written the bases in the brackets, its obvious which ones they are.

2log(10)20- (log(10)5+log(10)8)

= log(10)400/ log(10) 40 = log(10) 40/log(10)4 = log(10)10/log(10)1

But the answer at the back is: log (10) 10=1

log(8)25 + log(8)10 - 3log(8)5 = log(8) 250/ log (8) 125

The answer at the back of the book is: log(8)2=1/3

Thank you very much!
wrong! - when you subtract logs you have to divide
log(10)(400/40) = log(10) 10 = 1

phil
4. (Original post by LondonBoy)
1. Write as a single Logarithm, then simplfy your answer

I have written the bases in the brackets, its obvious which ones they are.

2log(10)20- (log(10)5+log(10)8)

= log(10)400/ log(10) 40 = log(10) 40/log(10)4 = log(10)10/log(10)1

But the answer at the back is: log (10) 10=1

log(8)25 + log(8)10 - 3log(8)5 = log(8) 250/ log (8) 125

The answer at the back of the book is: log(8)2=1/3

Thank you very much!
2log(10)20 - (log(10)5+log(10)8)
= log(10)20² - (log(10)[8x5])
= log(10)400 - log(10)40
= log(10)[400/40]
= log(10)10 = 1

log(8)25 + log(8)10 - 3log(8)5
= log(8)(25x10) - 3log(8)5
= log(8)250 - log(8)5³
= log(8)[250/5³]
= log(8)2
=> 8x = 2
x = log2/log8 = log2/log2³ = log2/3log2 = 1/3
5. (Original post by Phil23)
log(10)(400/40) = log(10) 10 = 1
wrong! - when you subtract logs you have to divide

phil
i love your posts.
6. (Original post by chewwy)
i love your posts.
cheers - you understand the second qeustion? cant make mistakes like that, lol - its reckless maths

pk
7. Im still so confused on how you get from log10 400/ log10 40 to the next part

can someone please explain it

thanks!
8. (Original post by LondonBoy)
Im still so confused on how you get from log10 400/ log10 40 to the next part

can someone please explain it

thanks!
That expression should never appear

Look at the explanations above and the rules of logs used
9. Ohhh legend i get it thanks.

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