SOLUTION: I need some help on these problems. 1. y varies directly as x and inversely as the square root of w; write the sentence as an equation. 2. write 3^x=y in log form. 3. w

Algebra ->  Functions -> SOLUTION: I need some help on these problems. 1. y varies directly as x and inversely as the square root of w; write the sentence as an equation. 2. write 3^x=y in log form. 3. w      Log On


   

Question 148022: I need some help on these problems.
1. y varies directly as x and inversely as the square root of w; write the sentence as an equation.
2. write 3^x=y in log form.
3. write log 2^x=y in exponential form.
4. solve for x; 5x/6-x/3=1/6
thanks for the help
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
1. y varies directly as x and inversely as the square root of w; write the sentence as an equation.
y = kx/(sqrt(x))
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2. write 3^x=y in log form.
x = log(base3) y
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3. write log 2^x=y in exponential form.
10^y = 2^x
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4. solve for x; 5x/6-x/3=1/6
Multiply thru by 6 to get:
5x - 2x = 1
3x = 1
x = 1/3
=================
Cheers,
Stan h>

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1
When "y varies directly as x", this means that as x increases y increases. Also as x decreases y decreases. So the first equation is y=kx. If let k be any number and you plug in values of x (say 1,2,3, etc), you'll notice that y will increase along with x.


Furthermore, when varies inversely as the square root of w, this means that as the square root of w increases y decreases. Also as square root of w decreases y increases. So the second equation is y=k%2Fsqrt%28w%29.

Now if you combine the two equations, you get

y=%28kx%29%2F%28sqrt%28w%29%29


So the entire sentence "y varies directly as x and inversely as the square root of w" translates to y=%28kx%29%2F%28sqrt%28w%29%29
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# 2

3%5Ex=y Start with the given equation.

log%283%2C%28y%29%29=x Rewrite the equation using the property: b%5Ey=x ===> log%28b%2C%28x%29%29=y


So the equation in logarithmic form is log%283%2C%28y%29%29=x



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# 3


log%2810%2C%282%5Ex%29%29=y Start with the given equation.


10%5Ey=2%5Ex Rewrite the equation using the property: log%28b%2C%28x%29%29=y ====> b%5Ey=x


So the equation in exponential form is 10%5Ey=2%5Ex


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# 4


5x%2F6-x%2F3=1%2F6 Start with the given equation.


6%285x%2Fcross%286%29-x%2Fcross%283%29%29=cross%286%29%281%2Fcross%286%29%29 Multiply both sides by the LCD 6 to clear any fractions.


5x-2x=1 Distribute and multiply.


3x=1 Combine like terms on the left side.


x=%281%29%2F%283%29 Divide both sides by 3 to isolate x.


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Answer:

So the answer is x=1%2F3


Which approximates to x=0.333