Question

Use properties of logs to expand the expression and simplify. log3(81 ⁵√ x²/ ³√y

a. 4+2/5. log₃x-1/3. log₃y
b. 2/5.log₃x-1/3. log₃y
c. 4-2/5. log₃x+1/3. log₃y
d. 2/5.log₃x+1/3. log₃y

Answer 1

To expand and simplify the expression, we can use properties of logarithms such as log(a/b) = log a - log b and log(xy) = log x + log y. After applying these properties and performing necessary calculations, the expression simplifies to log₃(x²/ya).

Step-by-step explanation:

To expand and simplify the expression log₃(81 ⁵√ x²/ ³√ya. 4+2/5. log₃x-1/3. log₃yb. 2/5.log₃x-1/3. log₃yc. 4-2/5. log₃x+1/3. log₃yd. 2/5.log₃x+1/3. log₃y,

1. We can start by using the property of logarithms that states log a - log b = log(a/b).
2. Next, we can use the property that states log(xy) = log x + log y to expand the expression further.
3. Then, we can simplify the expression by performing any necessary calculations.

Applying these steps to the given expression, the expanded and simplified form is log₃(x²/ya).