Evaluate log5 8 + log5 10 - 2 log5 20
You are correct. Using the logarithmic rules we can apply the formula loga (1/x) = -loga (x), which gives:
log5 (1/5) = -log5 5 = -1
Therefore, the evaluated expression is -1. Thank you for pointing out the oversight.
why stop there?
log5 (1/5) = -1
Log5 8 + log5 10 - 2log5 20= -1
I apologize for the mistake in my previous response. You are correct that the expression log5 8 + log5 10 - 2 log5 20 evaluates to -1.
Using logarithmic rules, we can simplify the expression as follows:
log5 8 + log5 10 - 2 log5 20
= log5 (8 * 10) - log5 (20^2)
= log5 80 - log5 400
= log5 (80/400)
= log5 (1/5)
= -1
Therefore, the evaluated expression is -1.
To evaluate the expression log5 8 + log5 10 - 2 log5 20, we can use the properties of logarithms.
The first property we can use is the product rule, which states that logb (M * N) = logb M + logb N. By applying this rule, we can rewrite the expression as:
log5 (8 * 10) - 2 log5 20
Simplifying further, we have:
log5 80 - 2 log5 20
Now, let's apply another property called the power rule, which states that logb (M^k) = k logb M. In this case, we can rewrite log5 80 as log5 (16 * 5), since 16 * 5 equals 80:
log5 (16 * 5) - 2 log5 20
Using the product rule again, we can split log5 (16 * 5) into log5 16 + log5 5:
(log5 16 + log5 5) - 2 log5 20
Next, we can apply the power rule to log5 16, as 16 can be express as 4^2:
(2 log5 4 + log5 5) - 2 log5 20
Using the log5 4 to log5 2 can be expressed as 2^2:
(2(2 log5 2) + log5 5) - 2 log5 20
Now, we can simplify the expression further:
(4 log5 2 + log5 5) - 2 log5 20
Finally, if we can evaluate the log5 2, log5 5, and log5 20, we can substitute the values to find the final result.
Using logarithmic rules, we can simplify the expression:
log5 8 + log5 10 - 2 log5 20 = log5 (8*10) - log5 (20^2)
= log5 (80) - log5 (400)
= log5 (80/400)
= log5 (1/5)
Therefore, the evaluated expression is: log5 (1/5)