Question

Log3 ( x+2 ) < 3 help help

Answer 1

Log₃(x+2)<3. 3=log₃3³=log₃27
log₃(x+2)<log₃27
основание логарифма a=27. 27>1, знак неравенства не меняем

$\left \{ {{x+2\ \textless \ 27} \atop {x+2\ \textgreater \ 0}} \right. \left \{ {{x\ \textless \ 25} \atop {x\ \textgreater \ -2}} \right.$

x∈(-2;25)

Answer 2

Understanding the Inequality Expression

The given expression is Log3(x + 2) < 3. This is an inequality expression involving a logarithmic function. Let's break down the components and understand the meaning of this expression.

Interpretation of the Inequality

The inequality Log3(x + 2) < 3 can be interpreted as finding the values of x for which the base-3 logarithm of (x + 2) is less than 3.

Explanation of the Solution

To solve this inequality, we need to find the values of x that satisfy the given inequality. This involves understanding the properties of logarithmic functions and applying them to the given expression.

Solution Process

The solution process involves understanding the behavior of logarithmic functions and applying the rules of inequalities to find the valid range of values for x that satisfy the given inequality.

Applying the Rules of Logarithmic Inequalities

To solve the inequality Log3(x + 2) < 3, we can apply the properties of logarithmic functions, such as the relationship between logarithmic expressions and exponential expressions, to find the range of values for x that satisfy the inequality.

Conclusion

In conclusion, the inequality Log3(x + 2) < 3 involves finding the values of x for which the base-3 logarithm of (x + 2) is less than 3. The solution process requires applying the rules of logarithmic inequalities to determine the valid range of values for x that satisfy the given inequality.