Logarithm Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Solve log⁡3(2x+1)=4\log_3(2x + 1) = 4.

Solution

  1. 1
    Convert to exponential form: 2x+1=34=812x + 1 = 3^4 = 81.
  2. 2
    Solve: 2x=802x = 80, so x=40x = 40.
  3. 3
    Check: log⁡3(2(40)+1)=log⁡3(81)=log⁡3(34)=4\log_3(2(40) + 1) = \log_3(81) = \log_3(3^4) = 4 ✓

Answer

x=40x = 40
To solve a logarithmic equation, convert it to exponential form using the definition log⁡ba=c⇔bc=a\log_b a = c \Leftrightarrow b^c = a, then solve the resulting algebraic equation.

About Logarithm

The logarithm log⁡b(x)\log_b(x) answers: "to what power must bb be raised to produce xx?" It is the inverse function of f(x)=bxf(x) = b^x.

Learn more about Logarithm →

More Logarithm Examples

Example 1 easy

Evaluate [formula].

Example 3 easy

Evaluate [formula].

Example 4 medium

Solve [formula] where [formula] denotes [formula].

Example 5 hard

Solve [formula].

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