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Antilog Calculator

Enter a base and an exponent to get the antilogarithm, b raised to y.

Calculate
A positive number other than 1. You can type e, 1/2 or 1.05.
Any number, for example 2.5 or -3.
Try:

Antilogarithm

antilog⁡10(52)=316.227766017\operatorname{antilog}_{10}(\frac{5}{2}) = 316.227766017antilog10​(25​)=316.227766017

316.227766017

The antilog of log b of x is x again.

Step by step

  1. 1Definition of the antilogarithm
    antilog⁡10(y)\operatorname{antilog}_{10}(y)antilog10​(y)
    ↓
    10y10^{y}10y

    The antilog undoes the log: it raises the base to the power.

  2. 2Substitute
    10y10^{y}10y
    ↓
    1052=316.22776601710^{\frac{5}{2}} = 316.2277660171025​=316.227766017
  3. 3Through the natural log
    10y=eyln⁡1010^{y} = e^{y \ln 10}10y=eyln10
    ↓
    e2.5×2.30258509299=316.227766017e^{2.5 \times 2.30258509299} = 316.227766017e2.5×2.30258509299=316.227766017

    How a calculator computes a power with a decimal exponent.

  • Definitionlog⁡bx=y  ⟺  by=x\log_b x = y \iff b^{y} = xlogb​x=y⟺by=x
  • Productlog⁡b(xy)=log⁡bx+log⁡by\log_b(xy) = \log_b x + \log_b ylogb​(xy)=logb​x+logb​y
  • Quotientlog⁡b ⁣(xy)=log⁡bx−log⁡by\log_b\!\left(\frac{x}{y}\right) = \log_b x - \log_b ylogb​(yx​)=logb​x−logb​y
  • Powerlog⁡b(xn)=nlog⁡bx\log_b(x^{n}) = n\log_b xlogb​(xn)=nlogb​x
  • Change of baselog⁡bx=ln⁡xln⁡b=log⁡10xlog⁡10b\log_b x = \frac{\ln x}{\ln b} = \frac{\log_{10} x}{\log_{10} b}logb​x=lnblnx​=log10​blog10​x​
  • Same baselog⁡bb=1,log⁡b1=0\log_b b = 1,\qquad \log_b 1 = 0logb​b=1,logb​1=0
  • Inverseblog⁡bx=x,log⁡b(bx)=xb^{\log_b x} = x,\qquad \log_b\left(b^{x}\right) = xblogb​x=x,logb​(bx)=x
  1. Tools
  2. Mathematics
  3. Logarithm Calculator
  4. Antilog Calculator

About Antilog Calculator

This antilog calculator undoes a logarithm. The antilog of y in base b is b raised to the power y, so the antilog of 2.5 in base 10 is about 316.23. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.

The page opens on base 10 and y = 2.5, giving about 316.227766017. Integer exponents give exact answers, such as the antilog of 3 in base 10, which is 1000, and the antilog of -3 in base 2, which is 1/8.

Use it to turn a log back into a number: if log10(x) = 2.5, then x is the antilog, 316.23. For the natural antilog, enter e as the base.

How to use Antilog Calculator

  1. 1Choose a mode: log of any base, ln, log10, log2, antilog or solve b^x = y.
  2. 2Enter the base (not needed for ln, log10 and log2) and the number. You can type fractions like 1/8, powers like 2^10 or the constant e.
  3. 3Read the exact or decimal answer at the top.
  4. 4Open the steps for the definition, the change of base and, when the number is an integer, the product and power rules applied to its prime factors.
  5. 5For an exponential equation such as 1.05^x = 2, choose Solve b^x = y.

Features

  • Log of any base, with exact rational answers when the number is an exact power of the base.
  • Natural log, common log and binary log as one-click modes.
  • Antilogarithm: b raised to the power y, exact for integer exponents.
  • Solve b^x = y, the form of compound interest, growth and half-life questions.
  • Change-of-base steps using both ln and log10.
  • Product and power rules shown on the prime factors of an integer argument.
  • Related logs in bases e, 10 and 2, and a list of the logarithm rules.
  • Plain explanations of domain errors.

Antilogarithm

The antilog is exponentiation.

antilog_b(y) = b^y
b^(log_b x) = x

Worked examples

  • antilog10 2.5 → gives ≈ 316.227766017

    10^2.5 = 10² × 10^0.5.

  • antilog2 -3 → gives 1/8

    2^-3 = 1/8.

Privacy: how it works

  • Everything is calculated by code running in your browser tab. The numbers you enter are not sent to Ulkaa or to any other server, and there is nothing to sign in to.

Tips

  • To check a log, raise the base to your answer. It should give back the number.
  • log of a number between 0 and 1 is negative, and log of 1 is 0 in every base.
  • For doubling time at a rate r per period, solve (1 + r)^x = 2 with the Solve mode.

Frequently asked questions

Is it really free?

Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.

Do I need an account?

No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.

Does it run in my browser?

Yes. Numbers are processed by code running in your browser tab, on your own device.

Is my data uploaded?

No. Numbers are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.

What is the antilog of a number?

It is the base raised to that number. The antilog of 3 in base 10 is 10³ = 1000.

How do I find the natural antilog?

Use base e: the natural antilog of y is e^y. Type e in the base box.

More Logarithm Calculator pages

  • Logarithm CalculatorPick the logarithm you need, enter the base and the number, and get the answer with the change-of-base working.
  • Natural Log CalculatorEnter a positive number to get ln(x), the logarithm to base e.
  • Log Base 2 CalculatorEnter a positive number to get log2(x), how many times you can halve it.
  • Log Base 10 CalculatorEnter a positive number to get log10(x), the common logarithm.
  • Change of Base CalculatorEnter a base and a number to see log_b(x) worked out with the change-of-base formula.
  • Solve Exponential EquationsEnter a base b and a target y to solve b^x = y for x.

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