Question

Logarithm help?

Answer 1

logx to the base 2 = a means the number is x=2^a

log a + log b = log(ab) adding logs is the same as log of their product

take antilog of all the values in your equation

(2^15)(2^14)/(2^105) = x

x = 2^(29-105) = 2^(-76) = (1/2)^76

Answer 2

Can you explain it in even more detail because I'm completely lost?

Answer 3

@tkhunny @mathmale

Answer 4

we are going to solve the problem by converting log x to x,
this is done by taking the anti-log of each term
for base 2 logarithms, the anti log of (log z) is 2^z.

Answer 5

Oh okay I think I get it now my brain was registering getting rid of the log all together. Thank you!

Answer 6

you could also do this
\[\log(15)+\log(14)-\log(105)=\log(\frac{15\times 14}{105})\]

Answer 7

since \(\frac{15\times 14}{105}=2\) you have
\[\log(2)=\log(x)\] making \(x=2\)
the base is not important in this question, would work the same way for any base