Question

Log2,6(8−x)−1>0 решите неравенство

Answer 1

8-х=2,6
х=5,4
одз 8-х≥0
х≤8
5,4 подходит!

Answer 2

To solve the inequality $\log_{2,6}(8-x) - 1 > 0$, we first need to understand that $\log_{2,6}(8-x)$ represents the logarithm of $(8-x)$ to the base $2,6$.

To simplify the inequality, follow these steps:

Step 1: Add 1 to both sides of the inequality to isolate the logarithm term: $\log_{2,6}(8-x) > 1$

Step 2: Rewrite the inequality in exponential form using the definition of logarithms: $2,6^1 < 8-x$

Step 3: Simplify the left-hand side: $2,6 < 8-x$

Step 4: Now, isolate the $x$ term by subtracting 8 from both sides: $2,6 - 8 < -x$

Step 5: Flip the inequality sign when multiplying/dividing by a negative number: $-5,4 > x$

So, the solution to the inequality is $x < -5,4$.