Question

Use properties of logarithms lne⁴+lne⁹-lne⁵

Answer 1

Using the properties of logarithms, lne⁴ + lne⁹ - lne⁵ can be simplified to 8.

Step-by-step explanation:

Using the properties of logarithms:

1. The sum of logarithms of two numbers is the logarithm of their product. So, lne⁴ + lne⁹ = ln(e⁴ * e⁹)
2. The logarithm of any number raised to an exponent is the product of the exponent and the logarithm of the number. So, ln(e⁴ * e⁹) - lne⁵ = (4 * ln(e)) + (9 * ln(e)) - ln(e⁵)
3. The natural logarithm of e is 1, so we can simplify further: (4 * 1) + (9 * 1) - ln(e⁵) = 4 + 9 - ln(e⁵)
4. The natural logarithm of e⁵ is 5, so the final expression is: 4 + 9 - 5 = 8

Therefore, lne⁴ + lne⁹ - lne⁵ equals 8.