Question

***** 3lg2/2lg2 *****

Answer 1

3/2=1.5 .............

Answer 2

To simplify the expression "3lg2/2lg2," I assume that "lg" represents the logarithm base 2. If that's the case, the expression can be simplified as follows:

3lg2 / 2lg2

Since the base of the logarithm is the same (base 2), we can use the property of logarithms that says:

a * log_b(x) = log_b(x^a)

Applying this property to the expression:

3lg2 / 2lg2 = lg2^(3/2)

Now, using the property of exponents that states:

a^(m/n) = (a^(1/n))^m

We can rewrite lg2^(3/2) as:

lg2^(3/2) = (lg2^(1/2))^3

Now, let's find the square root of 2 (lg2^(1/2)):

lg2^(1/2) = 2^(1/2) = √2

Finally, substitute back into the previous expression:

(lg2^(1/2))^3 = (√2)^3 = 2^(3/2) = √(2^3) = √8 = 2√2

So, the simplified expression for "3lg2/2lg2" is "2√2."