whats the answer to : log -subscript 1/5- (4) =?

To the four decimal places. How do I use a calculator and the base change formula to get this.

2 Answers

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  • gile
    Lv 7
    7 years ago

    log[base 0.2] (4) = log (4)/log (0.2)

    . . . . . . . . . . . . = log(2²)/log(2/10)

    . . . . . . . . . . . . = 2log(2)/[log(2) - log(10)]

    . . . . . . . . . . . . = 2log(2)/[log(2) - 1]

    . . . . . . . . . . . . = 2*0.30103/(0.30103 - 1)

    . . . . . . . . . . . . = 0.60206/(-0.69897)

    . . . . . . . . . . . . = -0.86135

    Rounded to the fourth decimal place:

    log[base 0.2] (4) = -0.8614

  • log[a](b) => log[c](b) / log[c](a)

    log[1/5](4) =>

    log(4) / log(1/5) =>

    -log(4) / log(5) =>

    -0.86135311614678610134021313752793

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