How do you solve log5 sqrt125?
Note:
we solve an equation for an unknown, and we simplify an expression.
Simplify:
log5√125
=log5√(5³)
= 3
(125 = 5³, so log5125=3, just like log1010³=3)
To solve the expression "log5 sqrt125," we follow these steps:
Step 1: Simplify the expression within the logarithm.
The square root of 125 is the same as raising 125 to the power of 1/2. Thus, sqrt125 can be rewritten as 125^(1/2).
Step 2: Apply the logarithmic property.
According to the logarithmic property, log(base b) a^c = c * log(base b) a. We can use this property to simplify the expression.
Using this property, we can rewrite log5 sqrt125 as (1/2) * log5 125.
Step 3: Evaluate the logarithm.
Now, we need to evaluate log5 125. This means finding the exponent to which we need to raise 5 to get 125.
Let's break down the number 125 into prime factors: 125 = 5 * 5 * 5 = 5^3.
So, log5 125 is equal to 3, since 3 is the exponent to which we need to raise 5 to get 125.
Step 4: Substitute the evaluated value back into the expression.
Taking the value we found in Step 3, we substitute it back into the expression:
(1/2) * 3 = 3/2.
Therefore, log5 sqrt125 is equal to 3/2, or 1.5.