Question

If log,a 2 = x and log,b 3 = y, which expression is equal to log,a 24=?
А=3+x
B=3+ y
C =3x + y
D=x+3y​

Answer 1

Answer:

$log(a \times 2) = x \\ log(a) + log(2) = x \\ now \\ log(b \times 3) = y \\ log(b) + log(3) = y \\ we \: have \: to \: find \: \\ log(a \times 24) = log(a) + log(24) \\ = x - log(2) + log( {2}^{3} \times 3) \\ = x - log(2) + log( {2}^{3} ) + log(3) \\ = x + log( \frac{ {2}^{3} }{2} ) + log(3) \\ = x - log( {2}^{2} ) + log(3) \\ = x - 2 \times log(2) + log(3) \\ = x - 2(x - log(a) ) + y - log(b) \\ = x - 2x + log(a) + y - log(b) \\ = y - x + log(a) - log(b)$

SORRY NOT ABLE TO UNDERSTAND WHAT YOU ASKED

• WRITE THE LOG TERM CORRECTLY