First, simplify the numerator:
3lg 2 - lg 24= lg (2^3) - lg 24= lg 8 - lg 24= lg (8/24)= lg (1/3)
Now, simplify the denominator:
lg 3 + lg 27= lg (3*27)= lg 81= 2
Now, divide the numerator by the denominator:
lg (1/3) / 2= lg (1/3 * 1/100)= lg (1/300)≈ -2.5229
Therefore, (3lg 2 – lg 24) / (lg 3 + lg 27) is approximately -2.5229.
First, simplify the numerator:
3lg 2 - lg 24
= lg (2^3) - lg 24
= lg 8 - lg 24
= lg (8/24)
= lg (1/3)
Now, simplify the denominator:
lg 3 + lg 27
= lg (3*27)
= lg 81
= 2
Now, divide the numerator by the denominator:
lg (1/3) / 2
= lg (1/3 * 1/100)
= lg (1/300)
≈ -2.5229
Therefore, (3lg 2 – lg 24) / (lg 3 + lg 27) is approximately -2.5229.