How Do You Evaluate a Logarithm Using Technology?

Enter the positive number into the appropriate logarithm function on your graphic display calculator (GDC): use log for base 10 and ln for base $e$. The displayed value is the exponent to which the base must be raised to produce the original number.

How the Calculation Works

A logarithm reverses exponentiation. The statement

$$\log_a(b)=x$$

means

$$a^x=b.$$

For example, to evaluate $\log_{10}(1000)$, enter log(1000) into the GDC. It returns $3$, because $10^3=1000$.

For a natural logarithm, enter ln(7). The GDC gives

$$\ln(7)=1.94591\ldots\approx1.95$$

to three significant figures. This means $e^{1.94591\ldots}=7$.

When the result is not exact, record enough digits before rounding. For example, $\log_{10}(37)=1.56820\ldots$, so the final answer is $1.57$ to three significant figures. You can verify it by evaluating $10^{1.56820\ldots}$, which returns approximately . This reverse check is especially useful if you accidentally select instead of .

A calculator may also offer a logarithm template with a base box. For this syllabus skill, however, you should recognize the dedicated base-10 and natural-logarithm keys first.

Always identify the base before choosing the calculator function. If no base is displayed, log conventionally means base 10 in this IB topic, while $\ln$ always means base $e$.

The input must be positive: $b>0$. Therefore, expressions such as $\log(0)$ and $\ln(-4)$ have no real value. A common misconception is that a negative logarithm is impossible. This is incorrect: $\log(0.01)=-2$ is valid because the input is positive and .

IB Exam Technique

This is SL 1.5, Exponents and Logarithms, common to SL and HL. For an SL Paper 1-style response, show the mathematical expression before the GDC value, keep full calculator precision during working, and round only the final answer as instructed, normally to three significant figures. Every Mathematics AI paper is GDC-active, but calculator notation alone is not an acceptable final answer.