Use properties of logarithms to expand the logarithmic expression as much as pos

Question

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)

Explanation / Answer

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 ab = 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. loga x3 = 3loga x

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