Log 4 + log25
10. 10
log 4 + log 25 is equal to log (4 * 25), which simplifies to log 100.
Using the logarithmic identity log a + log b = log (a * b), we can combine the logarithms of 4 and 25. Since 4 multiplied by 25 equals 100, log 4 + log 25 simplifies to log 100.
Therefore, log 4 + log 25 = log 100.
Step 1: Start with the given expression: log 4 + log 25.
Step 2: Use the properties of logarithms to simplify. The property states that log a + log b = log(a * b).
So, log 4 + log 25 can be rewritten as log(4 * 25).
Step 3: Simplify the product of 4 and 25. They multiply to give 100.
Therefore, log 4 + log 25 is equal to log 100.
Step 4: Simplify further by using another property of logarithms. The property states that log a to the base b = x can be rewritten as b^x = a. In this case, we have log 100, which means 100 is the result of raising 10 to the power of x.
So, 10^x = 100.
Step 5: Determine the value of x by finding the exponent that 10 needs to be raised to in order to get 100. Since 10^2 = 100, x is equal to 2.
Therefore, log 4 + log 25 is equal to log 100, which is equivalent to 2.
To simplify the expression log 4 + log 25, we can use the logarithmic rule that states the sum of the logarithms of two numbers is equivalent to the logarithm of their product.
So, we can rewrite the expression as log (4 * 25).
To simplify further, we can multiply 4 and 25, which gives us 100.
Therefore, log (4 * 25) is equal to log 100.
Finally, we can evaluate log 100 using another logarithmic rule that states the logarithm of a number raised to a power is equivalent to the product of the power and the logarithm of the number.
Since 10 raised to the power of 2 is equal to 100, we can rewrite log 100 as 2 * log 10.
The logarithm of 10 to any base is equal to 1, so log 10 is equal to 1.
Therefore, 2 * log 10 is equal to 2.
So, the simplified expression for log 4 + log 25 is 2.