Write the expression in terms of common logarithms, and then give a calculator approximation (correct to four decimal places).
log_(7) \(80\)
To write the expression in terms of common logarithms, we can use the formula:
logₐ (b) = log (b) / log (a)
Therefore, we can write:
log₇ (80) = log (80) / log (7)
Now, we can use a calculator to find the approximate value. Here are the steps to follow:
1. Enter "80".
2. Take the natural logarithm of 80 by pressing the "ln" or "log" button on your calculator.
3. Divide the result by the natural logarithm of 7. If your calculator doesn't have a natural logarithm button, you can use the common logarithm (log base 10) instead.
4. Round the result to four decimal places.
Using a calculator, the approximate value of log₇ (80) is 1.2702.