logs please help!?

Question

write as one logarithm
log(base2)X +3log(base2)y-1/2log(base2)X

ok so iknow i somehow have to get hte number infrot of the logs out of there but where does it go does it become an exponent? please help me

Answer 1

If the expression is

log(base2)X+3log(base2)y-(1/2)log(base2)X

First collect the like terms

log(base2)X +3log(base2)y-(1/2)log(base2)X

= (1/2)log(base2)X +3log(base2)y

Then apply the rule k*log(base n)X = log(base n)(X^k)

= log(base2)[X^(1/2)] + log(base2)(y^3)

Finally apply the rule

log(base2)X + log(base2)Y = log(base2)(X*Y)

= log(base2)([X^(1/2)]*y^3)

Answer 2

log a + log b = log (a*b)

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

a * log b = log (b^a)