Evaluating logarithms using change-of-base formula

Evaluating logarithms using change-of-base formula

Lessons

• change-of-base rule:
logba=logxalogxb=logalogb \log_ba = \frac{\log_xa}{\log_xb} = \frac{\log a}{\log b}

• common logarithms:
log with base 10" ``10"
example: log3=log103 \log3 = \log_{10}3
example: logx=log10x \log x = \log_{10}x
  • 1.
    How to apply `` change-of-base rule""

    Express log53 \log_53 in three different ways.

  • 2.
    Using a calculator, evaluate the following logarithms
    by applying `` change-of-base rule":":
    a)
    log53\log_53

    b)
    log7416\log_7\sqrt{416}

    c)
    log2725\log_2\frac{7}{25}

    d)
    6log4999 \log_4999


  • 3.
    Using a calculator, solve for x x to the nearest hundredth.
    a)
    log6x=log78\log_6x = log_7 8

    b)
    log235=logx0.104\log_{23}5 = log_x\sqrt{0.104}