Express log_5 288 in terms of decimal logarithms log2 and log3 Assuming a=log2 and b=log3 (log is the base 10 logarithm). I have to find log_5 288. How can I do this?

bsmart36

bsmart36

Answered question

2022-08-11

Express log 5 288 in terms of decimal logarithms log 2 and log 3
Assuming a = log 2 and b = log 3 (log is the base 10 logarithm). I have to find log 5 288. How can I do this?
I've tried transforming log 2 to log 5 2 log 5 10 and same for b. Then it's
5 log 5 2 + 2 log 5 3 log 5 10 = log 5 288 log 5 10 = 5 log 2 + 2 log 5 = 5 a + 3 b
Is that correct?

Answer & Explanation

Zechariah Zavala

Zechariah Zavala

Beginner2022-08-12Added 14 answers

HINT:
Using
log a b = log c b log c a ,
log 5 288 = log 5 ( 2 5 3 2 ) = 5 log 5 2 + 2 log 5 3 = 5 log 10 2 + 2 log 10 3 log 10 5
Now 1 = log 10 10 = log 10 2 + log 10 5 log 10 5 = 1 log 10 2 =
fotaczkak4

fotaczkak4

Beginner2022-08-13Added 3 answers

log 5 288 = log 10 288 log 10 5 = log 10 ( 2 2 2 2 2 3 3 ) log 10 ( 10 / 2 ) = log 10 2 + log 10 2 + log 10 2 + log 10 2 + log 10 2 + log 10 3 + log 10 3 + log 10 10 log 10 2 = log 10 2 + log 10 2 + log 10 2 + log 10 2 + log 10 2 + log 10 3 + log 10 3 + 1 log 10 2

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