Question

2log50=3 log 25+log(x-2) helppppp please

Answer 1

log(a) + log(b) = log(ab)
log(c) - log(d) = log(c/d)

Answer 2

and also

alog(b) = log(b^a)

Answer 3

2log50=3 log 25+log(x-2)

2log50-3 log 25=log(x-2)

now use log(c) - log(d) = log(c/d)

Answer 4

your job is to write
\[\log(x-2)=\log(whatever)\] so you can set
\[x-2=whatever\] and solve

Answer 5

before that use alog(b) = log(b^a)

Answer 6

The key to this problem is simplifying the left hand side after you isolate the term with the x on the right.\[2\log50=3 \log 25+\log(x-2) \implies 2\log50-3 \log 25=\log(x-2)\]\[\log50^2- \log 25^3=\log(x-2) \implies \log(\frac{50^2}{ 25^3})=\log(\frac{4}{25})=\log(x-2)\]\[\implies \frac{4}{25}=x-2 \implies \frac{54}{25}=x\]

Answer 7

If you don't simplify, the numbers in the fraction get discouragingly large.