who can help me thanks Maths problems?

Tutor: None Selected Time limit: 1 Day

If Logx (1 / 8) = - 3 / 2, then x is equal to?

Dec 22nd, 2014

We can apply the base-change rule on the left side so we have base 10 logs and the "x" is now inside a log instead of being a base of one: 

log(1/8) / log(x) = -3/2 

Now we can multiply both sides by log(x) 

log(1/8) = -3 log(x) / 2 

Now multiply both sides by -2/3 to get the log(x) by itself: 

-2/3 log(1/8) = log(x) 

If you are multiplying something by a log, it's the same as moving the coefficient inside the log as the exponent. You usually use this rule to move an exponent out, but in this case, we want it in: 

a log(x) = log(x^a) 

So now we have: 

log[(1/8)^(-2/3)] = log(x) 

Set both sides to be an exponent of a base of 10, which will remove the logs from both sides: 

x = (1/8)^(-2/3) 

Now, simplify this. First, resolve the negative exponent by taking the reciprocal of the base: 

x = 8^(2/3) 

Now change it to radical form since you have a fractional exponent: 

x = ³√(8)² 

You can take the cube root of 8: 

x = 2² 

And finally: 

x = 4

Dec 22nd, 2014

Dec 22nd, 2014
Dec 22nd, 2014
Oct 26th, 2016
Mark as Final Answer
Unmark as Final Answer
Final Answer

Secure Information

Content will be erased after question is completed.

Final Answer