Compute log7^6 .
Round your answer to 3 decimal places.
log 7^6
= 6log7
= ...
If you have a calculator handy, I don't,
type it
log7
=
x
6
=
thanks
To compute log7^6, we can use the logarithmic property which states that loga(b^c) = c * loga(b).
In this case, we have log7^6. Applying the property mentioned above, we get:
log7^6 = 6 * log7
Now we need to find the value of log7. We can use a calculator or a mathematical table to find the logarithm of 7. However, if you don't have access to those resources, we can approximate the value using the following steps:
1. Start with an initial guess for the logarithm of 7. Let's say log7 ≈ 0.9
2. Take this initial guess and raise 7 to that power: 7^0.9 ≈ 5.6234
3. Compare the result with the target value 7. If it's smaller, increase the guess; if it's larger, decrease the guess.
4. Keep repeating steps 2 and 3, adjusting the guess each time, until you get a value close enough to 7.
Doing this iteration manually, we can find that log7 ≈ 0.845.
Now we can substitute this value back into the equation:
log7^6 = 6 * log7 ≈ 6 * 0.845 ≈ 5.070
Finally, rounding the answer to 3 decimal places, we get log7^6 ≈ 5.070.