How do you evaluate #antilog 0.33736#?

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Answer 1 · 2017-05-02T18:28:05

The inverse of a logarithm is exponentiation with its base.

For example the inverse of the base 10 logarithm, (#log_10(x)#), is #10^(log_10(x))# by the definition of any inverse this always gives us x:

#10^(log_10(x)) = x#

Another example

#2^(log_2(x))=x#

Suppose that we have an equation:

#log_3(x-1) = 4#

Make both sides of the equation an exponent of the base, 3:

#3^(log_3(x-1)) = 3^4#

The left side becomes the argument within the logarithm, x -1:

#x-1 = 3^4#

The right side becomes 81:

#x-1 = 81#

Add 1 to both sides:

#x = 82#

Another example with base e:

#ln(x+2) = 2#

Make both sides and exponent of the base, e:

#e^(ln(x+2)) = e^2#

The left side becomes #x+2#:

#x+2 = e^2#

Subtract 2 from both sides:

#x = e^2-2#

I hope that this helps