Solving exponential equations

Solve for x:

\[3^{x+1} + 3^x = 324\]

3^(x+1) + 3^x = 324 <=> (3^x)*3 + 3^x = 324 <=> (3^x)( 3 + 1) = 324 <=> (3^x)*4 = 324 <=> 3^x = 81 <=> 3^x = 3^4 <=> x = 4.

Answered by crisforp | 2024-06-10

3 x + 1 + 3 x = 324 3 ⋅ 3 x + 3 x = 324 3 x ⋅ ( 3 + 1 ) = 324 4 ⋅ 3 x = 324 / : 4 3 x = 81 3 x = 3 4 ⟺ x = 4

Answered by Anonymous | 2024-06-10

To solve the equation 3 x + 1 + 3 x = 324 , we can rewrite it to find that x = 4 . This is done through factoring and isolating the term 3 x , which simplifies to 3 4 . Hence, we conclude that the solution is x = 4 .
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Answered by Anonymous | 2025-01-14