Question

Order the steps to solve the equation

log(x^2-15)= log(2x) form 1 to 5

x^2-2x-15=0
Potential solutions are -3 and 5
x^2-15=2x
x-5=0 or x+3=0
(x-5)(x+3)=0

Answer 1

Explanation:

When the base of a logarithm is not specified, it is assumed that the base is 10. Therefore we have:

`log_1_0(x^2-15)=log_1_0(2x)`

Intuitively you can see that if the two arguments inside of the logarithm equal each other, then both sides will be equal to each other. Therefore, you can say the following requirement:

`x^2-15=2x`

Subtract 2x on both sides to get:

`x^2-2x-15=0`

Use the quadratic formula to solve for 'x' to get:

`x=(-b+√(b^2-4ac) )/2a`

`x=(-b-√(b^2-4ac) )/2a`

Beginning with the first solution:

`x=(-(-2)+√((-2)^2-4(1)(-15)) )/2(1)`

`x=2+√(4+60) )/2`

`x=(2+√(64)) /2`

`x=(2+8)/2`

`x=5`

Second solution:

`x=(-(-2)-√((-2)^2-4(1)(-15)) )/2(1)`

`x=(2-√(4+60) )/2`

`x=(2-8)/2`

`x=-6/2`

`x=-3`

Since the 'x' value inside of the logarith is squared, the -3 is a valid solution. Ordinarily, the log function cannot take on negative values.