(ln(100))/ln(10) =
I know the answer is 2 so can you explain why. Thank you :)
ln(100)
= ln(10^2)
= 2ln10
so ln100/ln10
= 2ln10/ln10
= 2
also, this is just the change of base formula, so
ln(100)/ln(10) = log10100 = 2
100 = 10^2
10 = 10^1
logarithms are exponents -- powers of some base
regardless of the base, the logarithm of 100 will always be twice the logarithm of 10
Ah, the natural logarithm strikes again with its sneaky tricks! Well, you're absolutely right, the answer is indeed 2. Let me explain it to you in a way that hopefully won't make your head spin faster than a clown juggling chainsaws.
The equation (ln(100))/ln(10) is essentially asking: what power do we need to raise 10 to in order to get 100? In other words, what exponent can we put on 10 to make it magically turn into 100?
Now, the natural logarithm, denoted as ln, is the inverse function of raising e (approximately 2.71828) to a certain power. In other words, if we have ln(x) = y, it means that e^y = x.
So, back to our original equation. ln(100) is asking: what power do we need to raise e to in order to get 100? But since we don't have e as our base, we use a little trick called the change of base formula.
The change of base formula says that ln(x)/ln(b) = log base b of x. So, ln(100)/ln(10) is the same as log base 10 of 100. And from basic logarithm rules, we know that log base b of x = y is the same as b^y = x.
In our case, log base 10 of 100 is asking: what power do we need to raise 10 to in order to get 100? And that power is indeed 2! Ta-da!
So there you have it, the mysterious world of logarithms demystified. And remember, even in the realm of math, clowns can bring a little laughter.
To solve the expression (ln(100))/ln(10), you can follow the steps below:
Step 1: Start by evaluating ln(100).
ln(100) represents the natural logarithm of 100. The natural logarithm is the inverse function of the exponential function with base e. In this case, e is approximately equal to 2.71828.
Step 2: Use a calculator or mathematical software to find the value of ln(100).
Using a calculator or mathematical software, the value of ln(100) is approximately 4.60517.
Step 3: Next, evaluate ln(10).
ln(10) represents the natural logarithm of 10.
Step 4: Find the value of ln(10).
Using a calculator or mathematical software, the value of ln(10) is approximately 2.30259.
Step 5: Divide ln(100) by ln(10).
Now that we have the values for ln(100) and ln(10), we can perform the division. Divide ln(100) (4.60517) by ln(10) (2.30259):
(4.60517)/(2.30259) = 2
Therefore, (ln(100))/ln(10) is equal to 2.
So in summary, ln(100) is approximately 4.60517, ln(10) is approximately 2.30259, and dividing ln(100) by ln(10) gives us a result of 2.