Use properties of logarithms to expand the logarithmic expre

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log(x/10,000) log(x/10,000) = Use properties of logarithms to expand the logarithmic expression as much as possible. Evaluate logarithmic expressions without using a calculator if possible. In(e^3/13) In(e^3/13) = 0,43505 Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log_a x^3 log_a x^3 = IN(x^3)/IN(4)

Solution

3. log (x/10000) = log (x/10⁴ ) = log x – log x⁴ = log x – 4log 10 = log x – 4 = lox x – 0.6021 ( as log a/b = log a – log b ; log a^b = b log a and log 10 = 1)

4. ln(e³ / 13) = lne³ – ln13 = 3 ln e – 2.5649 = 3 - 2.5649 = 0.4351 ( as ln e = 1)

5. log_a x³ = 3log_a x