Simplify
(Log75+log9+log5)÷(log5+log45)
(Log75+log9+log5)÷(log5+log45)
= log(75*9*5) / log(5*45)
= log 3375 / log 225
= log(25*9*15) / log(25*9)
= log(5^2 * 3^2 * 15)/log(5^2 * 3^2)
= log( 15^2 * 15) / log (15^2)
= (log 15^2 + log 15)/ log 15^2
= (2log15 + log15)/(2log15)
= 3log15/(2log15)
= 3/2
I think I could probably shorten this up a bit.
1.5
To simplify the expression, let's use the properties of logarithms.
We know that log(a) + log(b) = log(ab) and log(a) - log(b) = log(a/b).
So, we can rewrite the expression as:
(Log75+log9+log5) / (log5+log45)
Using the property log(a) + log(b) = log(ab), we can rewrite the numerator as:
log(75 * 9 * 5) / (log5+log45)
Further simplifying, we get:
log(3375) / (log5+log45)
Now, let's use the property log(a) + log(b) = log(ab) again to simplify the denominator:
log(3375) / log(5 * 45)
Simplifying further, we have:
log(3375) / log(225)
Finally, we can rewrite log(3375) as log(225 * 15), using the property log(a) + log(b) = log(ab):
log(225 * 15) / log(225)
Now, let's simplify log(225 * 15) again:
log(3375) / log(225)
Using one final property, log(a) - log(b) = log(a/b), we can rewrite the expression as:
log(3375 / 225)
Simplifying the numerator and denominator, we get:
log(15)
Therefore, the simplified expression is log(15).
To simplify the expression (log75 + log9 + log5) ÷ (log5 + log45), we can use the properties of logarithms.
1. Start by applying the product property of logarithms, which states that log(a) + log(b) is equal to log(a * b).
We can rewrite the expression as:
log(75 * 9 * 5) ÷ log(5 * 45)
2. Simplify the numerator and denominator by calculating the products:
log(3375) ÷ log(225)
3. Next, apply the quotient property of logarithms, which states that log(a) ÷ log(b) is equal to log base b of a.
The expression becomes:
log base 225 of 3375
4. Simplifying further, determine what exponent we need to raise 225 to in order to obtain 3375.
225^x = 3375
We find that 225 raised to the power of 2 equals 3375.
Therefore, the simplified expression is log base 225 of 3375 = 2.