Find the value of the following.
10^(-10log3)
The log exponent is confusing me. Could someone please help me? Thanks.
-10log3= log3^-10= log (1/3^10)
so 10^(log(1/3^10)= 1/3^10
Here is an unconfusing explanation.
log100=2
so 10^2=l0^(log100) by definition.
Have you come across the property of logs that says ..
a^loga k = k
your question fits that pattern after a quick adjustment
10^(-10log3)
= 10^(log 3^(-10))
= 3^-10
= 1/3^10 , so far no calculator
= appr. .000016935
check:
log3 = .47771213
-10log3 = -4.771213
10^-4.771213 = .00016935
Thanks!
Sure! I'd be happy to help you understand how to find the value of 10^(-10log3).
To evaluate this expression, we need to understand the properties of logarithms and exponents.
First, let's start by simplifying the expression inside the parentheses: -10log3.
The notation "log3" refers to the logarithm of 3 with base 10. In other words, it represents the power to which we need to raise 10 to get 3.
The negative sign (-) in front of "10log3" tells us to take the negative of the value obtained from the logarithm.
So, to find the value of "-10log3", you need to calculate the logarithm of 3, multiply it by -10, and then negate the result.
Once you have the value of "-10log3", you can substitute it back into the original expression: 10^(-10log3).
Now, let's walk through the steps to find the value of this expression:
Step 1: Calculate the logarithm of 3 using base 10:
log3 = log(3) base 10 ≈ 0.4771 (rounded to four decimal places)
Step 2: Multiply the logarithm by -10:
-10 * 0.4771 ≈ -4.771 (rounded to four decimal places)
Step 3: Negate the result from Step 2:
-(-4.771) = 4.771
Step 4: Substitute the value from Step 3 back into the original expression:
10^4.771
Step 5: Finally, evaluate the expression using a calculator:
10^4.771 ≈ 57379.4 (rounded to one decimal place)
So, the value of 10^(-10log3) is approximately 57379.4.
Please note that the final value is rounded to one decimal place for simplicity.
I hope this explanation helps you understand how to find the value of the given expression! Let me know if you have any further questions.