use the properties of logarithms to simplify the logarithmic expression.
log10 (9/300)
Please explain!!
Crazy how +11 years later and I have the same question.
Lmao it's been over 12 years nvm
Subtracting logs is the equivalent of dividing.
log 9 - log 300 = ??
I think they want you to show the two values as 9=3^2 and 300=3x10^2
so you have
log 3^2 - log(3x10^2)
=2 log 3 - (log3 + 2log10)
can you take it from here?
To simplify the logarithmic expression log10 (9/300), we can apply the properties of logarithms.
The quotient rule states that logb(p/q) is equal to logb(p) - logb(q), where b is the base of the logarithm.
In this case, we have log10 (9/300). Using the quotient rule, we can write this as:
log10 (9) - log10 (300)
Now, we can further simplify each term separately.
First, let's simplify log10 (9). Since the base is 10, we are looking for the exponent that 10 must be raised to in order to obtain 9. Mathematically, we can express this as:
10^x = 9
Taking the logarithm of both sides with base 10, we get:
x = log10 (9)
So, log10 (9) is equal to the exponent x. Therefore, log10 (9) simplifies to x.
Now, let's simplify log10 (300) using the same process. We have:
10^x = 300
Taking the logarithm of both sides with base 10, we get:
x = log10 (300)
So, log10 (300) simplifies to x.
Putting it all together, our original expression log10 (9/300) can be written as:
log10 (9) - log10 (300)
which simplifies to:
x - x = 0
Therefore, the simplified form of log10 (9/300) is 0.