Use log5(2)=0.4307 and log5(3)=0.6826 to approximate the value of log5=54.
According to the example in my book I would divide 0.6826 by 0.4307 and the answer is 1.5848 but this is not one of the answers given.
My choices are:
a) 0.1370
b) 2.4785
c) 0.8820
d) 0.7488
Where did I go wrong?
Thanks
Solve pls
Well, it seems like you've fallen into a mathematical circus act! Let me help you out of this clownish confusion.
To find the value of log5(54), we can use the property of logarithms that says log5(54) = log5(2 * 3^3).
Now, let's break it down! We know that log5(2) = 0.4307 and log5(3) = 0.6826. So using these values, we can rewrite log5(54) as:
log5(54) = log5(2 * 3^3) = log5(2) + log5(3^3)
Substituting the given values, we get:
log5(54) = 0.4307 + 0.6826 * 3
Calculating this, we find:
log5(54) ≈ 0.4307 + 2.0478 ≈ 2.4785
So, the answer that matches this approximation is option b) 2.4785.
Don't worry, my mathemagical friend. Sometimes the circus can be confusing, but with a little bit of clowning around, we can find the right answer!
To approximate the value of log5(54), you can use the logarithmic properties to rewrite it as:
log5(54) = log5(2 * 3^3)
Using the logarithmic property log(a * b) = log(a) + log(b), we can further simplify this to:
log5(54) = log5(2) + log5(3^3)
Now, substitute the given values:
log5(54) ≈ 0.4307 + 0.6826 * 3
Multiply 0.6826 by 3:
log5(54) ≈ 0.4307 + 2.0478
Adding these two values together, we get:
log5(54) ≈ 2.4785
Therefore, the correct answer is b) 2.4785.
It seems you made a mistake in your division. Instead of dividing 0.6826 by 0.4307, you should have added it to the product of 0.6826 and 3.
54 = 2*3*3*3
log 54 = log 2 + 3 log 3
= .4307 + 3(.6826)
= 2.4785
Well, at least I agree with one of them !