Question

7log9 162/7log9 2 как решить

Answer 1

Log(9)162/2 = log(9)81 = log(9)9² = 2*log(9)9 = 2*1 = 2.
семёрки сократить можно было..
ответ : 2.

Answer 2

To solve the expression 7log₉(162) / 7log₉(2), we can use the properties of logarithms. Remember that logₐ(b) represents the logarithm of b with base a.

Step 1: Simplify the expression inside each logarithm.

log₉(162) can be simplified as follows: 162 = 2 × 3² × 3⁴ = 2 × 3⁶ log₉(162) = log₉(2 × 3⁶)

log₉(2) remains unchanged.

Step 2: Use the logarithmic property logₐ(b) = logₐ(c) + logₐ(d) if the argument is multiplied: logₐ(b * c) = logₐ(b) + logₐ(c).

Therefore, the expression becomes: 7log₉(2 × 3⁶) / 7log₉(2)

Step 3: Use the logarithmic property logₐ(b^c) = c * logₐ(b) if the argument is raised to a power: logₐ(b^c) = c * logₐ(b).

Now, the expression becomes: 7 * 6log₉(3) / 7log₉(2)

Step 4: The 7 in the numerator and denominator cancel out.

The final simplified expression is: 6log₉(3) / log₉(2)

This is the simplest form of the expression. If you need a numerical approximation, you can calculate the logarithms using a calculator.