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Question 1164541: Your friend claims you can use the change - of - base to write the
expression (In x) as a common logarithm. Is your friend correct?
Explain your reasoning.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! yes, he is correct.
y = ln(x) is the same as y = loge(x)/log(e).
take x = 1525
ln(1525) = 7.329749689
log(1525) / log(e) = the same.
the derivation of the log base conversion is as follows:
y = ln(x) if and only if e^y = x
take the log of both sides of the equation to get:
log(e^y) = log(x)
since log(e^y) = y * log(e), you get:
y * log(e) = log(x)
solve for y to get:
y = log(x) / log(e)
since they're both equal to y, you get:
ln(x) = log(x) / ln(x)
that's the base conversion formula that says loga(x) = logb(x) / logb(a)
this is useful to convert all different bases to base 10.
for example:
2^5 = 32
this is true if and only if log2(32) = 5
log function of your calculator gets you log to the base of 10, i.e. log10.
you use your calculator log function to get:
log2(32) = log(32)/log(2).
log(32)/log(2) = 5
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