expand ln22x ln3xy^3 thanks :)

ln22x = ln22 + lnx

ln3xy^3 = ln3 + lnx + 3lny

Ln 22 wx vc sjed

To expand ln(22x), we need to use logarithmic properties to simplify the expression. The property we'll use is ln(a) + ln(b) = ln(ab).

Step 1: Start with the given expression - ln(22x).

Step 2: Notice that 22 can be factored into 2 * 11, and x can be written as x^1. So, we can write ln(22x) as ln(2 * 11 * x).

Step 3: Apply the logarithmic property. ln(2 * 11 * x) can be written as ln(2) + ln(11) + ln(x).

Hence, the expanded form of ln(22x) is ln(2) + ln(11) + ln(x).

Now, let's expand ln(3xy^3) using the same approach.

Step 1: Start with the given expression - ln(3xy^3).

Step 2: Notice that 3 can't be factored further, x and y can be written as x^1 and y^3 respectively. So, we can write ln(3xy^3) as ln(3 * x * y^3).

Step 3: Apply the logarithmic property. ln(3 * x * y^3) can be written as ln(3) + ln(x) + ln(y^3).

Step 4: Further simplification is possible. Recall the logarithmic property ln(a^b) = b * ln(a). By applying this property on ln(y^3), we get 3 * ln(y).

Hence, the expanded form of ln(3xy^3) is ln(3) + ln(x) + 3 * ln(y).

I hope this explanation helps! Let me know if you have any further questions.