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

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) (Show Source): You can put this solution on YOUR website!

Applying logarithms to both sides we get

Logarithm of a product is the sum of the logarithms, so we can write that as

Logarithm of a power is the exponent multiplied by the logarithm of the base, so we can write that as

It's plain algebra from now on. Subtracting
Dividing both sides by (-4) we get
or

That would be enough to get an approximate answer for the value of
If we want an exact answer we can apply some more logarithm properties.
We know that , so we can write the equation above as
and since as

Because logarithm of a power is the exponent multiplied by the logarithm of the base, so we can write that as
So
or
For a more elegant way to express the value of x,

So
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