Logarithm and Exponent Calculator: Log to Any Base, Solve b^x = y, Growth, Decay and Doubling Time
Logs, exponents and exponential growth and decay in one place.
Engineering student calculators
Free textbook calculators with every step shown, so you can check your own working. Pick one, type in your numbers and see the formulas worked out. Or switch to Ask a question for an explained answer. No account needed.
Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.
How this calculator works
Choose log, solve, or growth and decay.
For a log enter the base and the number. To solve b to the power x equals y enter b and y.
For growth enter the starting amount, the percent change per period and the number of periods.
Formulas used
- \log_bx = \frac{\ln x}{\ln b}
- b^x = y\ \Rightarrow\ x = \frac{\ln y}{\ln b}
- P = P_0(1 + r)^t
- t_2 = \frac{\ln2}{\ln(1 + r)}
Worked example
With the default numbers in the calculator above:
- The logarithm: 3.00 (so 2 to the power 3.00 is 8)
- Natural log and log to base 10 of the number: 2.08 and 0.90
- Check: 8.00
Change the numbers in the calculator to see the full working, every step, for your own case.
A second worked example
A different case, with these numbers: What do you want? Solve b^x = y for x; Base 10; The number (log case) or the value y (solve case) 5000.
- Solve b^x = y by taking logs of both sides: 3.70
- Check: 5000.00
Common questions
What is a logarithm?
The power to which the base must be raised to give the number. log base 2 of 8 is 3 because 2 cubed is 8.
How do I find a log to a base my calculator does not have?
Use the change of base formula: divide the natural log of the number by the natural log of the base.
What is the rule of 72?
The doubling time in periods is about 72 divided by the percent growth per period.
Related calculators
Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Any school or first-year mathematics text (logarithms and exponentials).
Need a calculator we do not have?
Embed this calculator on your own page
Copy this code into your page. The calculator runs inside the frame and links back to Drafting Central.
Need this drawn, designed or checked?
Drafting Central is a mechanical engineering and drafting business working with customers across Australia and around the world. A calculator gives you the numbers; we can turn them into drawings and designs.
Need help with a real project?
Talk to Drafting Central →