Exponential Function Math Example 2

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

Example 2

medium
Solve 32xโˆ’1=813^{2x - 1} = 81.

Solution

  1. 1
    Express 81 as a power of 3: 81=3481 = 3^4.
  2. 2
    Set exponents equal: 2xโˆ’1=42x - 1 = 4.
  3. 3
    Solve: 2x=52x = 5, so x=52x = \frac{5}{2}.

Answer

x=52x = \frac{5}{2}
When both sides of an equation can be written with the same base, equate the exponents. This technique avoids needing logarithms.

About Exponential Function

An exponential function has the form f(x)=aโ‹…bxf(x) = a \cdot b^x where b>0b > 0, bโ‰ 1b \neq 1. The variable is in the exponent, not the base.

Learn more about Exponential Function โ†’

More Exponential Function Examples

Example 1 easy

A bacteria population starts at 500 and doubles every 3 hours. Write an exponential model and find t

Example 3 medium

A radioactive substance has a half-life of 10 years. If the initial amount is 200 g, how much remain

Example 4 hard

Two bacteria colonies start with 100 and 500 cells respectively. Colony A doubles every 3 hours; Col

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