QuestionDecember 13, 2025

Solve the equation for C. 2-b=log(9c+5) C= square

Solve the equation for C. 2-b=log(9c+5) C= square
Solve the equation for C.
2-b=log(9c+5)
C= square

Solution
4.3(219 votes)

Answer

c = \frac{10^{\,2 - b} - 5}{9} Explanation 1. Isolate the logarithmic term \log(9c + 5) = 2 - b We keep the log on one side. 2. Convert logarithm to exponential form 9c + 5 = 10^{\,2 - b} Using definition of log base 10: \log x = y \implies x = 10^y. 3. Solve for c 9c = 10^{\,2 - b} - 5 c = \frac{10^{\,2 - b} - 5}{9}

Explanation

1. Isolate the logarithmic term<br /> $ \log(9c + 5) = 2 - b $ <br />We keep the log on one side.<br /><br />2. Convert logarithm to exponential form<br /> $ 9c + 5 = 10^{\,2 - b} $ <br />Using definition of log base 10: $\log x = y \implies x = 10^y$.<br /><br />3. Solve for $c$<br /> $ 9c = 10^{\,2 - b} - 5 $ <br />$ c = \frac{10^{\,2 - b} - 5}{9} $
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