Question

Log0.5(4x-1)-log0.5(7x-3)=0

Answer 1

Log0,5((4x-1)/(7x-3))=log0,5(1)

(4x-1)/(7x-3)=1
4x-1=7x-3
3x=2
x=2/3

Answer 2

To solve the logarithmic equation, we'll use logarithm properties to combine the logarithms into a single expression. The general rule we'll use is:

log_a(x) - log_a(y) = log_a(x/y)

Let's apply this rule to the given equation:

log0.5(4x - 1) - log0.5(7x - 3) = 0

log0.5((4x - 1) / (7x - 3)) = 0

Now, we can rewrite the equation in exponential form:

0.5^0 = (4x - 1) / (7x - 3)

Since 0.5^0 equals 1, we have:

1 = (4x - 1) / (7x - 3)

Now, we'll solve for x:

Multiply both sides by (7x - 3) to eliminate the fraction:

7x - 3 = 4x - 1

Move all x terms to one side and constant terms to the other side:

7x - 4x = -1 + 3

3x = 2

Divide by 3 to solve for x:

x = 2 / 3

So, the solution to the equation is:

x = 2 / 3