How to Put Log4 17 in Calculator

Calculating logarithms with different bases can be confusing, but this guide will show you exactly how to put log4 17 in a calculator and understand the result.

How to Calculate log4 17

The expression log4 17 means "the logarithm of 17 with base 4". This is asking the question: "To what power must 4 be raised to get 17?"

Most scientific calculators can compute logarithms with different bases, but if your calculator only has log (base 10) and ln (natural logarithm), you'll need to use the change of base formula.

Change of Base Formula:

log_b a = ln a / ln b

Or: log_b a = log₁₀ a / log₁₀ b

For log4 17, you would use either:

ln(17) / ln(4)
log(17) / log(4)

Step-by-Step Calculation

Enter the number 17 into your calculator
Press the log button (for base 10) or ln button (for natural log)
Store this result in memory (if your calculator has memory functions)
Clear the calculator and enter the number 4
Press the log or ln button again
Recall the stored value from step 3
Divide the two results (stored value ÷ current value)

If your calculator has a "log" function with a base selector, simply enter 17, select base 4, and press log.

The Formula

The general formula for calculating logarithms with any base is:

log_b a = ln a / ln b

Or: log_b a = log₁₀ a / log₁₀ b

Where:

b = base of the logarithm (4 in our case)
a = the number you're taking the logarithm of (17 in our case)

Worked Example

Let's calculate log4 17 using the change of base formula with natural logarithms:

Calculate ln(17) ≈ 2.833213344056216
Calculate ln(4) ≈ 1.3862943611198906
Divide: 2.833213344056216 ÷ 1.3862943611198906 ≈ 2.0455

So, log4 17 ≈ 2.0455

This means 4².0455 ≈ 17

FAQ

Can I calculate log4 17 without a calculator?: Yes, using the change of base formula and logarithms tables, but it's much more time-consuming than using a calculator.
What does log4 17 mean?: It means "the power to which 4 must be raised to get 17".
Is log4 17 the same as ln 17 / ln 4?: Yes, this is the change of base formula that allows you to calculate logarithms with any base using only natural logarithms.
What if my calculator doesn't have a ln button?: You can use the base 10 logarithm (log) instead, using the formula log10(17)/log10(4).
How accurate is the result from a calculator?: Modern scientific calculators provide results accurate to at least 10 decimal places, which is usually sufficient for most practical purposes.