Question

Consider the equation and solution steps shown here. If there is an error, identify the step in which the error occurs.problem: 5^x+3 = 212step A: In 5^x+3 = In 212step B: x + 3(In 5) = In 212step C: x = In 212 - 3(In 5)A) step AB) step BC) step CD) no error

Answer 1

Solution:

Given the equation;

$5^{x+3}=212$

STEP A: Take the logarithm of both sides;

$\begin{gathered} \ln (5^{x+3_{}})=\ln (212) \\ \end{gathered}$

STEP B: Apply the logarithmic law;

$\log _ba^c=c\log _ba$

$\begin{gathered} \ln (5^{x+3_{}})=\ln (212) \\ (x+3)\ln (5)=\ln 212 \end{gathered}$

STEP C: Divide both sides by In(5);

$\begin{gathered} (x+3)\ln (5)=\ln 212 \\ \frac{(x+3)\ln (5)}{\ln (5)}=\frac{\ln 212}{\ln (5)} \\ x+3=\frac{\ln212}{\ln(5)} \end{gathered}$

Thus, there is an error in the solution.

CORRECT OPTION: B