Question

help..2lg6-lg3/lg144 plz

Answer 1

$\frac{2lg6-lg3}{lg144}=\frac{lg6^{2}-lg3}{lg144}=\frac{lg36-lg3}{lg144}=\frac{lg36/3}{lg144}=$

$=\frac{lg12}{lg12^{2}}=\frac{lg12}{2lg12}=\frac{1}{2}$

Answer 2

To solve the expression 2lg6-lg3/lg144, let's break it down step by step:

1. Simplify the expression inside the logarithm: lg6. The base of the logarithm is not specified, so we'll assume it is base 10. Therefore, lg6 is the logarithm of 6 to the base 10.

2. Use a calculator or a logarithm table to find the value of lg6. The value of lg6 is approximately 0.7782.

3. Simplify the expression inside the second logarithm: lg144. Again, assuming base 10, lg144 is the logarithm of 144 to the base 10.

4. Use a calculator or a logarithm table to find the value of lg144. The value of lg144 is approximately 2.1584.

5. Substitute the values of lg6 and lg144 back into the original expression: 2lg6-lg3/lg144.

- 2lg6 becomes 2 * 0.7782 which is approximately 1.5564. - lg3/lg144 becomes 0.7782 / 2.1584 which is approximately 0.3602.

6. Finally, substitute the values obtained in step 5 back into the original expression: 1.5564 - 0.3602.

- The result is approximately 1.1962.

So, the value of the expression 2lg6-lg3/lg144 is approximately 1.1962.

Please note that the values provided are approximate due to rounding.