Question

Lg x= lg(a2 - b2) - lg(a-b) + lg 2​

Answer 1

Lg x= lg(a2 - b2) - lg(a-b) + lg 2​

Lg x= lg((a - b)(a+b)) - lg(a-b) + lg 2​

Lg x= lg(2(a - b)(a+b) /(a-b))

Lg x= lg(2(a+b))

X=2(a+b), a>b.

Answer 2

To simplify the expression $\lg(x) = \lg(a^2 - b^2) - \lg(a - b) + \lg 2$, we can use logarithmic properties. Here are the steps to simplify it:

Step 1: Apply the quotient rule of logarithms: $\log_b(x) - \log_b(y) = \log_b\left(\frac{x}{y}\right)$.

Step 2: Apply the product rule of logarithms: $\log_b(xy) = \log_b(x) + \log_b(y)$.

Step 3: Simplify $a^2 - b^2$ using the difference of squares formula: $a^2 - b^2 = (a + b)(a - b)$.

Now, let's proceed with the simplification:

$\lg(x) = \lg(a^2 - b^2) - \lg(a - b) + \lg 2$

Using the difference of squares formula: $\lg(x) = \lg((a + b)(a - b)) - \lg(a - b) + \lg 2$

Now, applying the quotient rule and the product rule:

$\lg(x) = \lg\left(\frac{(a + b)(a - b)}{a - b}\right) + \lg 2$

$\lg(x) = \lg(a + b) + \lg 2$

Using the product rule:

$\lg(x) = \lg(2(a + b))$

Now, if the equation holds, we can drop the logarithms and equate the arguments:

$x = 2(a + b)$

So, the simplified equation is $x = 2(a + b)$.