If I have the question -> log10(221) = log10 13 + log10 17 - how do I prove it to be true or false?

Question

Thank you for your responses.

I really do hate Maths, and I have all these logarithms to do.

Now I have one's like x=log10 (7 to the power of 3) and x=loge(16 squared) where I need to find x.

I get that 7 to the 3 is 343. So do I put log of 343 on my calculator to get the x?

Answer 1

Note that 221 =13*17
and
log10(ab) =log10 a +log10 b
it's true

Answer 2

log10(221) = log10(13) + log10(17)

Rule 1 of logs:

Log[n](a*b) = log[n](a) + log[n](b)

Also 221 can be written as 17*13

So...

log10(221) = log10(17*13) = log10(17) + log10(13)

Which is what you were asked to prove/disprove, it is true.

For the second part just evaluate the part in the bracket, and take the log of the number to that particular base

x = log10(7^3)

x = 2.53529412

x = loge(16^2)

x = 5.545177444

Answer 3

It is true.
Rule
loga A + loga B = loga (AB)
Thus:-
log10 (13) + log10 (17) = log10 (221)

Answer 4

Summing logarithms is the same as multiplying numbers so
Log 13 + Log 17 = Log 221..............13 * 17 =221
1.1139 + 1.23 = 2.349

Answer 5

let a= log(10)13> 10^a=13
let b=log(10)17> 10^b=17
10^(a+b)=13x17=221
> a+b=log(10)221
>log(10)13+log(10)17=log(10)221