Log2+2log3
log2+log 3²
log(2•9)
log18


hence ans is "none of these"

To solve the given equation, let's break it down step by step:

Step 1: Rewrite the equation using the properties of logarithms
log2(2log3)

Step 2: Apply the exponentiation property of logarithms
2log3 = 3^2

Step 3: Simplify the expression
log2(3^2)

Step 4: Apply the power rule of logarithms
log2(9)

Step 5: Convert the logarithm base to the same base as the given options (base 10)
log10(9)/log10(2)

Now, let's evaluate this expression using a calculator:

log10(9) ≈ 0.9542
log10(2) ≈ 0.3010

Step 6: Divide the two logarithms
0.9542 / 0.3010 ≈ 3.1694

Therefore, the value of log2(2log3) is approximately 3.1694.

Now, let's determine which option among A, B, C, or D represents the value we obtained.

Option A: log150 ≈ 2.1761
Option B: log11 ≈ 1.0414
Option C: log25 ≈ 1.3979

None of these options match the value we calculated (3.1694). Therefore, the correct answer is D) None of these.

In conclusion, the value of log2(2log3) is approximately 3.1694, and the correct answer is D) None of these.