How many times do I have to tell you the answer is d. Goodness.
http://www.jiskha.com/display.cgi?id=1168934037
all you had to do was add two numbers given, and double it, and put the neg sign in front.
I have no idea what the answer to this problem is, I'm given choices but I'm still lost. Given: log sub a 2=.4, log sub a 3 =.5, log sub a 5=.8 what is log sub a .01?
a)0.7
b)-0.6
c)1.44
d)-2.4
Please Help!
I'm inclined to say .7 but it just a guess.
i need help by finding defenitions
To find the value of log sub a 0.01 using the given information, we need to use logarithmic properties and equations.
First, let's understand what log sub a means. "log sub a" is a logarithm with the base a. In this case, a is the base of the logarithm.
Now, let's look at the information given:
log sub a 2 = 0.4
log sub a 3 = 0.5
log sub a 5 = 0.8
We want to find log sub a 0.01.
To solve this problem, we can use the following property of logarithms: log(a^b) = b * log(a). This property states that the logarithm of a number raised to a power is equal to the product of that power and the logarithm of the number.
First, we can rewrite log sub a 0.01 as log(0.01)/log(a). This is because the logarithm of any number to the base a can be written as the logarithm of that number divided by the logarithm of the base.
To find log(0.01), we need to express 0.01 as a power of a. Since 0.01 = 1/100, we can rewrite it as (1/100)^1. Applying the logarithmic property, we have log(0.01) = 1 * log(1/100).
Next, we can rewrite 1/100 as (1/10)^2. Applying the logarithmic property again, we have log(1/100) = 2 * log(1/10).
Using the given information, we know that log sub a 10 = 1. We can rewrite log(1/10) as log(10^-1) = -1 * log(10).
Now, we can substitute the known values into the equation:
log sub a 0.01 = 2 * log(1/10) = 2 * (-1 * log(10)) = -2 * log(10).
Since we do not have the value of log sub a 10 directly, we need to find its value using the given information.
From the given information, log sub a 5 = 0.8. We can rearrange this equation to solve for log sub a 10.
If log sub a 5 = 0.8, then log sub a 5^2 = log sub a 25 = 2 * log sub a 5 = 2 * 0.8 = 1.6.
Since log sub a 10 is halfway between log sub a 5 and log sub a 25, we can estimate its value to be approximately 1.4.
Therefore, log sub a 0.01 is approximately -2 * log(10) which is approximately -2 * 1.4 = -2.8.
Based on the provided answer choices:
a) 0.7
b) -0.6
c) 1.44
d) -2.4
The closest answer to -2.8 is d) -2.4, which means the answer to the problem is d) -2.4.