Question

Log₃45+2log₃6-log₃20 решение

Answer 1

Держи) Если что-то непонятно – обращайся

Answer 2

To solve the expression, we'll use the properties of logarithms. The logarithm properties we'll use are:

1. logₐ(b) + logₐ(c) = logₐ(bc) - The sum of logarithms is equal to the logarithm of the product.
2. n * logₐ(b) = logₐ(bⁿ) - The coefficient of the logarithm is equivalent to the exponent of the term inside the logarithm.

Given expression: log₃45 + 2log₃6 - log₃20

Step 1: Simplify each logarithm term:

• log₃45 cannot be simplified further because 45 is not a power of 3 and cannot be expressed as a product of powers of 3.
• 2log₃6 can be simplified as follows: 2log₃6 = log₃6² = log₃36
• log₃20 cannot be simplified further for the same reason as log₃45.

Step 2: Substitute the simplified logarithms back into the expression: log₃45 + log₃36 - log₃20

Step 3: Combine the logarithms using the logarithm property: log₃(45 * 36) - log₃20

Step 4: Perform the arithmetic inside the logarithm: log₃(1620) - log₃20

Step 5: Apply the subtraction property of logarithms: log₃(1620/20)

Step 6: Simplify the expression inside the logarithm: log₃(81)

Step 7: The final result: log₃(81) = 4

Therefore, the solution to the expression is 4.