Write the expression as the sum or difference of two logarithmic functions conta

Steven Smith

Steven Smith

Answered question

2021-11-10

Write the expression as the sum or difference of two logarithmic functions containing no exponents.
log(xx+5)

Answer & Explanation

Wasither1957

Wasither1957

Beginner2021-11-11Added 17 answers

Step 1
To find an equlivalent expression in the required form
Step 2
General fact about logarithms
a=10m,b=10n,then
(by defination).
loga=m,logb=n
Note that log(ab)=log(10mn)
=mn=logalogb
Thus, log(ab)=logalogb
Step 3
Thus, the given expression has been expressed as the difference of two logarithms
log(ab)=logalogb
Thus,  log(xx+5)=logxlog(x+5)

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