Answer: x = 8
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I'm going to use the notation log(2,x) to indicate "log base 2 of x". The first number is the base while the second is the expression inside the log (aka the argument of the log)
log(2,x) + log(2,(x-6)) = 4
log(2,x*(x-6)) = 4
x*(x-6) = 2^4
x*(x-6) = 16
x^2-6x = 16
x^2-6x-16 = 0
(x-8)(x+2) = 0
x-8 = 0 or x+2 = 0
x = 8 or x = -2
Recall that the domain of log(x) is x > 0. So x = -2 is not allowed. The same applies to log(2,x) as well.
Only x = 8 is a proper solution.
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You can use the change of base rule to check your work
log base 2 of x = log(2,x) = log(x)/log(2)
log(2,(x-6)) = log(x-6)/log(2)
So,
(log(x)/log(2)) + (log(x-6)/log(2)) = 4
(log(8)/log(2)) + (log(8-6)/log(2)) = 4
(log(8)/log(2)) + (log(2)/log(2)) = 4
(log(2^3)/log(2)) + (log(2)/log(2)) = 4
(3*log(2)/log(2)) + (log(2)/log(2)) = 4
3+1 = 4
4 = 4
The answer is confirmed
Answer:
Sarah is making 4 batches of granola bars. She needs 7/8 cup peanuts to each batch and her measuring cup holds 1/8 cup.
Thus, if one cup holds then to make , Sarah will have to measure = 7 times for one batch of granola bars.
Therefore, for making 4 batches of granola bars, Sarah must measure 1/8 cup peanuts 7 x 4=28 times.Step-by-step explanation:
Answer:
(-6, 4)
Step-by-step explanation:
Pythagorean Theorem: a^2 + b^2 = c^2
a = 6
c = 9
b = ?
6^2 + b^2 = 9^2
36 + b^2 = 81
b^2 = 81 - 36
b^2 = 45
b = sqrt(45)
b = 6.71 miles
First you start off by setting up a Subtraction problem there anything common denominators of 7/8 and two over three verse 7/8 you should get 21/24 invert to over three you should get 16/24 then you would subtract those two anyway to get 5/24 I hope that was helpful get it
