Question 400998: Please show how to condense the following expressions:
2 log 9 + 5 log x + log 1/3
3 ln x + ln y + ln 10
2(ln2 - ln x) + (ln x - ln4)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Please show how to condense the following expressions:
2 log 9 + 5 log x + log 1/3
3 ln x + ln y + ln 10
2(ln2 - ln x) + (ln x - ln4)
rules to remember:
when multiplying numbers, add their logarithms
when dividing numbers, subtract their logarithms
for numbers with exponents, multiply exponent times logarithm of the number
first expression
2 log 9 + 5 log x + log 1/3
=log9^2+logx^5+log1-log3 (log 1 of any base=0)
=log9^2+logx^5-log3
=log((9^2)*(x^5)/3)
=log((81)*(x^5)/3)
=log(27*x^5)
second expression
3 ln x + ln y + ln 10
=lnx^3+lny+ln10
=ln(x^3*y*10)
third expression
2(ln2 - ln x) + (ln x - ln4)
=2ln2-2lnx+lnx-ln4
=2ln2-lnx-ln4
=2ln2-(lnx+ln4)
=ln(2^2/4x)
=ln(4/4x)
=ln(1/x)
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