Anonymous

How to find the antilog of 15.6?

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David Shabazi Profile
David Shabazi answered

I'm going to assume the base of the logarithm was 10 (which it should be. If the base isn't clarified in the problem, automatically assume it's ten.)

antilog(15.6) = x (antilog is the same as log inverse, denoted as log^-1. I'll be using that to replace antilog since that's how I learned it. We are also trying to find x.)

log^-1(15.6) = x

Take the logarithm of both sides, as shown:

log[log^-1(15.6)] = log(x)

The log and log^-1 cancel out on the left-hand side, so we remain with:

log(x) = 15.6

Raise both sides of the equation as powers for 10.

10^log(x) = 10^15.6

Since the base of the logarithm on the left-hand side of the equation is 10, and it's being raised as an exponent of 10, they cancel out.

(For those who are confused, think of e and natural logs. e to the power of ln x is equal to x, because the exponent of e also has a natural log with a base of e. Your precalculus teachers would've gone over this.)

x = 10^15.6

Therefore, the antilog of 15.6 is 10^15.6.

Tim Cook Profile
Tim Cook answered

For those of us who aren't as brilliant at math like David, then a question finding out the the antilog of 15.6 is going to have us scratching our heads! Luckily, there are several places online where we can get help.

If you are in a hurry, and just need the answer to the problem straight away, here are a couple of sites which can give you an instant answer to the question of the antilog of 15.6:

  • rapidtables.com/calc/math/anti-log-calculator
  • ncalculators.com/number-conversion/anti-log-logarithm-calculator
  • easycalculation.com/log-antilog.php

At each of these sites, you can input your own choice of base, if it isn't 10 as David has used in his answer. I have input 15.6 as the antilog of base 10 on each of these sites, which agreed the antilog of 15.6 is 3981071705534969.5.

If you need to know more about antilogs, and would like to work through some examples, try:

  • clas.sa.ucsb.edu/staff/lee/AntiLogs.htm (four examples of increasing difficulty)
  • ncalculators.com/math-worksheets/how-to-calculate-antilog.htm (an explantion using other bases aside from 10, and advice on how to calculate anitlogs for fractional numbers)
  • math.stackexchange.com/questions (contains a thread giving tips on how to use the antilog function on a calculator)
If you're still struggling, and I wouldn't blame you if you were, there's always YouTube, which has lots of useful tutorials about every math topic. Here's a clip on antilogs which should help:

Melwin Joseph Profile
Melwin Joseph answered
Raise 15.6 as the power value of the base.
10 ^ 15.6 = 3981071705534969.5 with the use of Antilog Calculator

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