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# 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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- gileLv 77 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

- 7 years ago
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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