z = log(5) [200/8] = log(5)[25]
5^z = 25
z = 2
log(5) 20 + log (5) 10 - 3log(5) 2?
5^z = 25
z = 2
First, let's recall the properties of logarithms:
1. Logarithm of a product: log(base a) (xy) = log(base a) x + log(base a) y
2. Logarithm of a quotient: log(base a) (x/y) = log(base a) x - log(base a) y
3. Logarithm of an exponent: log(base a) (x^y) = y * log(base a) x
Now, let's solve the given expression step by step:
1. log(base 5) 20 + log(base 5) 10 - 3 log(base 5) 2
2. Applying the logarithm of a product property to the first two terms:
log(base 5) (20 * 10) - 3 log(base 5) 2
3. Simplifying the product:
log(base 5) 200 - 3 log(base 5) 2
4. Applying the logarithm of an exponent property to the last term:
log(base 5) 200 - log(base 5) (2^3)
5. Simplifying the exponent:
log(base 5) 200 - log(base 5) 8
6. Using the logarithm of a quotient property:
log(base 5) (200/8)
7. Simplifying the division:
log(base 5) 25
8. Since 5^2 = 25, the final answer is 2.
Therefore, the solution to the given expression log(base 5) 20 + log(base 5) 10 - 3 log(base 5) 2 is equal to 2.