Given lgx + lg(x-1) = lg2, we can simplify it using property 1:
lg(x(x-1)) = lg2 lg(x^2 - x) = lg2
Now, to solve for x, we need to exponentiate both sides using base 10:
x^2 - x = 10^2 x^2 - x = 100
Rearranging the equation:
x^2 - x - 100 = 0
This is a quadratic equation that can be factorized or solved using the quadratic formula.
Similarly, to solve the second equation lg(5-x) + lg(x) = lg4, follow the same steps with the given properties of logarithms and then simplify the equation to solve for x.
To solve the first equation, we can use the properties of logarithms which state that:
1) lg(a) + lg(b) = lg(ab)
2) lg(a) - lg(b) = lg(a/b)
Given lgx + lg(x-1) = lg2, we can simplify it using property 1:
lg(x(x-1)) = lg2
lg(x^2 - x) = lg2
Now, to solve for x, we need to exponentiate both sides using base 10:
x^2 - x = 10^2
x^2 - x = 100
Rearranging the equation:
x^2 - x - 100 = 0
This is a quadratic equation that can be factorized or solved using the quadratic formula.
Similarly, to solve the second equation lg(5-x) + lg(x) = lg4, follow the same steps with the given properties of logarithms and then simplify the equation to solve for x.