SOLUTION: how do u solve?: 3.5x^-4 = 175 please show work i don't understand how to do it.

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Question 570808: how do u solve?: 3.5x^-4 = 175
please show work i don't understand how to do it.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
3.5x%5E-4+=+175
Applying logarithms to both sides we get
log%28%283.5x%5E-4%29%29+=log%28%28+175%29%29
Logarithm of a product is the sum of the logarithms, so we can write that as
log%28%283.5%29%29%2Blog%28%28x%5E-4%29%29+=log%28%28+175%29%29
Logarithm of a power is the exponent multiplied by the logarithm of the base, so we can write that as
log%28%283.5%29%29%2B%28-4%29log%28%28x%29%29+=log%28%28+175%29%29
It's plain algebra from now on. Subtracting
Dividing both sides by (-4) we get
log%28%28x%29%29+=%28log%28%28+175%29%29-log%28%283.5%29%29%29%2F%28-4%29 or
log%28%28x%29%29+=%28-1%2F4%29%28log%28%28+175%29%29-log%28%283.5%29%29%29
That would be enough to get an approximate answer for the value of x
If we want an exact answer we can apply some more logarithm properties.
We know that log%28%28a%2Fb%29%29=log%28%28a%29%29-log%28%28b%29%29, so we can write the equation above as
log%28%28x%29%29+=%28-1%2F4%29%28log%28%28+175%2F3.5%29%29%29 and since 175%2F3.5=50 as
log%28%28x%29%29+=%28-1%2F4%29%28log%28%28+50%29%29%29
Because logarithm of a power is the exponent multiplied by the logarithm of the base, so we can write that as
log%28%28x%29%29+=log%28%2850%5E%28-1%2F4%29%29%29 So
x=50%5E%28-1%2F4%29 or x=1%2Froot%284%2C50%29
For a more elegant way to express the value of x,

So highlight%28x=root%284%2C200%29%2F10%29