Question

Solve the following equations.
ln(10) − ln(7 − x) = ln(x)

Answer 1

the problem has two solutions x = 5, x = 2

Explanation:

Hello! To solve this equation we must find the value of X, this is initially done by applying the logarithm equations, the first one states that the subtraction of two logarithms is equal to their division

ln(10) − ln(7 − x) = ln(x)

`ln((10)/(7-x) )=lnx`

now we apply the euler exponential functions in order to eliminate logarithms

`e^{ln((10)/(7-x) )} =e^( lnx)\\(10)/(7-x) =x`

Now we apply algebra to find the value of X

`(10)/(7-x) =x\\10=(7-x)x\\10=7x-x^2\\x^2-7x+10=0`

finally we find the solutions of the resulting quadratic equation

x1=5

x2=2

the problem has two solutions x = 5, x = 2