SOLUTION: how can a negative antilog be solve?

Question 892149: how can a negative antilog be solve?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the definition of antilog from the dictionary is:

The number whose logarithm is a given number.

For example, the logarithm of 1,000 is 3 because 10^3 = 1000, so the antilogarithm of 3 is 1,000.

per the definition, it's the number whose logarithm is a given number.

the number is 1000.
the logarithm of 1000 is equal to 3.
the number whose logarithm to the base of 10 is 3, is 1000.

your question is how can a negative antilog be solved.

the log of a number can itself be negative.

for example, the log of (1/1000) is equal to -3 because 10^-3 = 1/1000.

to find the antilog of -3, you need to find the number whose logarithm is -3.

since the base is 10, you are then looking for 10^-3 = .001 = 1/1000.

another example:

log to the base of 2 of (1/32) is equal to -5 because 2^-5 = 1/2^5 = 1/32.

the antilog of -5 to the base of 2 is 2^-5 = 1/32.

1/32 is the antilog of -5 with a base of 2.

if the base is not 10, it needs to be specified.

antilog of -3 is assumed to be 10^-3 because the base was not specified and so it's assumed to be 10.

antilog of -5 to the base of 3 would be equal to 3^-5 = 1/3^5 = 1/243.

the antilog of -5 to the base of 3 would be equal to 1/243 because the log to the base of 3 of (1/243) is equal to -5.

you can find the log of another base other than 10 using your calculator by using the base conversion formula.

log of any base can be found using the base of 10 by the following conversion formula.

loga(x) = log10(x)/log10(a)

example:

log3(1/243) = log10(1/243)/log10(3) = LOG(1/243)/LOG(3), where LOG means log10 and LOG is the log key on your calculator.

try it on your calculator.

log3(1/243) = LOG(1/243)/LOG(3).

you will get -5.

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