Question

2+log√1+x+3log√1-x=log √1-x^2. Solve for x?

Answer 1

`x = 0.99`

Explanation:

I'm assuming you wish for us to solve

`2 + logsqrt(1 + x) + 3logsqrt(1 -x) = logsqrt(1 - x^2)`

We must apply the logarithm laws:

`2 + logsqrt(1 + x) + 3logsqrt(1 - x) = logsqrt((1 + x)(1 -x))`

`2 + 1/2log(1+ x) + 3/2log(1 -x) = 1/2log((1 + x)(1 -x))`

`2 + 1/2log(1+ x) + 3/2log(1- x) = 1/2log(1 + x) + 1/2log(1 -x)`

`log(1 - x) = -2`

`10^-2=1-x`

`x=1-10^-2`

`x = 1-1/100`

`x=99/100=0.99`

Hopefully this helps!