Math Problem Statement

Log3 (x+1)=2

Solution

We are given the equation:

log3(x+1)=2\log_3 (x+1) = 2

To solve this, we can rewrite the equation in its exponential form. The logarithmic equation logba=c\log_b a = c is equivalent to the exponential form a=bca = b^c. So:

x+1=32x + 1 = 3^2

Simplifying the right-hand side:

x+1=9x + 1 = 9

Now, subtract 1 from both sides to isolate xx:

x=91x = 9 - 1

x=8x = 8

Thus, the solution is:

x=8x = 8


Would you like more details or have any questions about the steps? Here are some related questions:

  1. How can you solve logarithmic equations with different bases?
  2. What is the inverse of a logarithmic function?
  3. How do you check the solution of a logarithmic equation?
  4. Can you solve a similar equation with a negative value inside the logarithm?
  5. How do logarithmic and exponential functions relate to each other?

Tip: Always check that the argument of the logarithm (inside the parentheses) is positive, as logarithms are undefined for non-positive numbers.

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Math Problem Analysis

Mathematical Concepts

Logarithms
Exponential Equations

Formulas

log_b(a) = c → a = b^c

Theorems

Logarithmic to Exponential Conversion

Suitable Grade Level

Grades 8-10