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