How do you express a sum of logarithms for log_5(125*25)log5(12525)?

2 Answers
Aug 7, 2018

log_5(125xx25) = log_5 125 + log_5 25log5(125×25)=log5125+log525

Explanation:

log_b (x xx y) = log_b x + log_b ylogb(x×y)=logbx+logby

log_5(125xx25) = log_5 125 + log_5 25 log5(125×25)=log5125+log525

"As a sum of logarithms: " log_5(125xx25) = log_5 125 + log_5 25As a sum of logarithms: log5(125×25)=log5125+log525

Aug 7, 2018

In support of mazoo's answer

Explanation:

color(blue)("Preliminaries")Preliminaries

Note that log_a(x) = log_10(x)/log_10(a)loga(x)=log10(x)log10(a)

Actually this still works if a=10a=10 as we have:

log_10(x)=log_10(x)/log_10(10) = log_10(x)/1log10(x)=log10(x)log10(10)=log10(x)1
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color(blue)("Looking at the question")Looking at the question

Known: 125xx25=3125125×25=3125

So we have: log_5(3125) log5(3125)

Converting to log base 10 this gives:

log_10(3125)/log_10(5) =(3.49485...) /(0.69897...)

log_10(3125)/log_10(5) =5" "............Solution(1)
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color(blue)("looking at mizoo's answer")

They state the answer as log_5(125)+log_5(25)

log_10(125)/log_10(5)+log_10(25)/log_10(5)

color(white)("ddd")3 color(white)("ddddd")+ color(white)("dd")2color(white)("dddd") = 5" "...Solution(2)

As both solutions 1 and 2 match it demonstrates that mazoo has shown the correct method