Question
Simplify the expression without a calculator. Assume each variable expression is defined for appropriate values of \( x \). \( 10^{\log (3 x+3)}= \)
Ask by Chadwick Lane. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 3x + 3 \)
Solution
Calculate or simplify the expression \( 10^{\log (3x+3)} \).
Simplify the expression by following steps:
- step0: Solution:
\(10^{\log_{10}{\left(3x+3\right)}}\)
- step1: Transform the expression:
\(3x+3\)
The simplified expression is \(3x+3\).
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Simplify this solution Bonus Knowledge
To simplify the expression \( 10^{\log (3x + 3)} \), we can use the property of logarithms that states \( 10^{\log_a(b)} = b \) when the base of the logarithm and the base of the exponent are the same. Thus, we have: \[ 10^{\log(3x + 3)} = 3x + 3. \] This means the expression simplifies directly to \( 3x + 3 \). Now you're ready to tackle problems like a pro!
