Question

if log 30 tothe base 6 is equal to a and log 24 to the base 15 is equal to b then find log 60 to base 12​

Answer 1

Step-by-step explanation:

hope it will help you

plzz mark me as a brainliest ❤❤❤

Answer 2

log630=a⇔a=log6+log5log6⇔(a−1)log6=log5.…(1)  

log1524=b⇔3log2+log3log3+log5=b⇔blog5=3log2−(b−1)log3.…(2)

Note that log6=log2+log3. We eliminate log3 from eqns. (1) and (2).

(b−1)log5b(a−1)log5=(a−1)(b−1)log2+(a−1)(b−1)log3=3(a−1)log2−(a−1)(b−1)log3.

Adding the two equations gives

(ab−1)log5=(ab+2a−b−2)log2.…(3)

From eqns. (1) and (3),

log12=log2+log6=(ab−1ab+2a−b−2+1a−1)log5=a2b+a−b−1(a−1)(ab+2a−b−2)log5=b(a+1)+1ab+2a−b−2log5.…(4)

Therefore,

log60=log12+log5=(b(a+1)+1ab+2a−b−2+1)log5=2ab+2a−1ab+2a−b−2log5.…(5)

From eqns. (4) and (5),

log6012=log12log60=ab+b+12ab+2a−1.