Ask Me Help Desk - Solving Calculus Logs

1. Log(2)5 +log(2)(X^2-1) - log(2) (X-1)

2. 3^log(3)5

3. 2log(10) root of X +3log(10) X^1/3

Solving for the indicated variable... solve this equation for A..

4.x/a + y/b + z/c=1

These problems cannot be solved! There isn't any equal sign. However, you may simplify them.

I'll not give you the answers, but will give you the properties of logs.

$log\, a + log\, b = log\, ab$

$log\, a - log\, b = log\, \frac ab$

$log\, a^b = blog\,a$

$log_b\, a = \frac{log\,a}{log\,b}$

If $x = log\,y$ , then $y = 10^x$

If $x = log_a\,y$ , then, $y = a^x$

For number four, once again, you cannot solve that. There are too many variables. However, you can make 'a' the subject of formula.

Quote:

Originally Posted by claire3158

1. $log_{2}(5) +log_{2}(x^{2}-1) - log_{2}(x-1)$
$\;\ \;\ \;\ \;\ \;\ \;\ \;\ \;\ \;\ \;\ \;\ \;\ \;\ \;\ \;\ \;\ \uparrow$
................Is this supposed to be an =?

If that - is supposed to be an =, then we can proceed as such by noting that the bases are all the same. That makes it easier.

$log(5)+log(x^{2}-1)=log(x-1)$

$log(5(x^{2}-1))=log(x-1)$

$5(x^{2}-1)=x-1$

$5x^{2}-x-4=0$

Solve the quadratic. Make sure to check both solutions by plugging them back into the equation. One may be extraneous.