Question

(log2 12-log2 3+3^log3 8)lg 5

Answer 1

(log2 12/3 + 8) log10 5= (log2 4 + 8) 1/2= (2+8)1/2= 10*1/2= 5

(легко так-то)

Answer 2

Let's break down the expression step by step:

1. log2 12: This represents the logarithm of 12 base 2. To simplify this, we can use the change of base formula:

   log2 12 = log10 12 / log10 2

   Evaluating log10 12 and log10 2 gives us approximately:

   log2 12 ≈ 3.58496 / 0.30103 ≈ 11.91886

2. log2 3: This represents the logarithm of 3 base 2. Similarly, we can use the change of base formula:

   log2 3 = log10 3 / log10 2

   Evaluating log10 3 and log10 2 gives us approximately:

   log2 3 ≈ 0.47712 / 0.30103 ≈ 1.58496

3. 3^log3 8: This is 3 raised to the power of the logarithm of 8 base 3. Let's evaluate log3 8 first:

   log3 8 = log10 8 / log10 3

   Evaluating log10 8 and log10 3 gives us approximately:

   log3 8 ≈ 0.90309 / 0.47712 ≈ 1.89279

   Now, we can calculate 3^log3 8:

   3^log3 8 = 3^1.89279 ≈ 6.86932

4. (log2 12 - log2 3 + 3^log3 8): Substituting the values we calculated in steps 1, 2, and 3:

   (log2 12 - log2 3 + 3^log3 8) ≈ (11.91886 - 1.58496 + 6.86932) ≈ 17.20322

5. lg 5: This represents the logarithm of 5 base 10. Evaluating this gives us:

   lg 5 ≈ log10 5 ≈ 0.69897

6. Finally, we calculate the expression (log2 12 - log2 3 + 3^log3 8)lg 5:

   (log2 12 - log2 3 + 3^log3 8)lg 5 ≈ 17.20322 * 0.69897 ≈ 12.01285

Therefore, (log2 12 - log2 3 + 3^log3 8)lg 5 is approximately equal to 12.01285.