SOLUTION: Using laws of logarithms, write the expression below using sums and/or differences of logarithmic expressions which do not contain the logarithms of products, quotients, or powers.

Question 1061258: Using laws of logarithms, write the expression below using sums and/or differences of logarithmic expressions which do not contain the logarithms of products, quotients, or powers. Enter the natural logarithm of x as ln(x) or log(x). Use decimals instead of fractions.
ln(x^3((sqrt(x-3)) / 4x+5) =
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
ln(x^3((sqrt(x-3)) / 4x+5) =
:
ln(x^3((sqrt(x-3)) - ln(4x+5) =
:
used logarithmic division rule
:
ln(x^3) + ln((x-3)^(1/2)) - ln(4x+5) =
:
used logarithmic multiply rule
:
3ln(x-3) + ln(x-3)/2 -ln(4x+5)
:
3ln(x)/ln(3) + ln(x)/2ln(3) - ln(4x+5)
:
Note 3/ln(3) = 2.7307, 1/2ln(3) = 0.4551
:
************************************
2.7307ln(x) + 0.4551ln(x) - ln(4x+5)
************************************
:

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