expand completely

Question

expand completely using the properties of logarithms.

𝑙𝑛 ( 𝑥 ^2 𝑦^ 4 / √𝑥−1 )

𝑙𝑜𝑔2 ( 𝑥 5 / √𝑦𝑧 4 )

Answer 1

𝑙𝑛 ( 𝑥 ^2 𝑦^ 4 / √𝑥−1 )

𝑙𝑛 ( 𝑥 ^2 𝑦^ 4 ) - ln √𝑥−1 )

𝑙𝑛 ( 𝑥 ^2) + ln (𝑦^ 4 ) - ln √𝑥−1 )

2 ln x + 4 ln y - (1/2) ln (x-1)

For the second exercise I have not very clear the form you wrote the exercise. This is what I understood. the "2" is the base of the log. the "5" and "4" are the exponents?

𝑙𝑜𝑔₂ ( 𝑥 ⁵ / √𝑦𝑧 ⁴ )

𝑙𝑜𝑔₂ 𝑥 ⁵ - log₂ √𝑦𝑧 ⁴

5 𝑙𝑜𝑔₂ x - log₂ (yz)²

5 𝑙𝑜𝑔₂ x - 2log₂ (yz)

5 𝑙𝑜𝑔₂ x - 2 ( log₂ y + log₂ z )

5 𝑙𝑜𝑔₂ x - 2 log₂ y - 2 log₂ z