SOLUTION: Please help me answer this question: If log3 (5)= a and log3 (6)=b, express log3 (20) in terms of a and b

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Question 1156480: Please help me answer this question:
If log3 (5)= a and log3 (6)=b, express log3 (20) in terms of a and b
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


If log%283%2C5%29=+a+
+log%283+%2C6%29=b+=> log%283+%2C2%2A3%29=b => log%283+%2C2%29%2Blog%283+%2C3%29=b=> log%283+%2C2%29%2B1=b=> +log%283+%2C2%29=b-1

express log%283+%2C20%29 in terms of a and b
log%283+%2C20%29+=log%283+%2C2%5E2%2A5%29+
log%283+%2C20%29+=log%283+%2C2%5E2%29%2Blog%283+%2C5%29+
log%283+%2C20%29+=2log%283+%2C2%29%2Blog%283+%2C5%29 .......substitute log%283+%2C2%29 and log%283+%2C5%29 from equations above

log%283+%2C20%29+=2%28b-1%29%2Ba
log%283+%2C20%29+=a%2B2b-1