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

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 \\ ((x+3)\ln (5))/(\ln (5))=(\ln 212)/(\ln (5)) \\ x+3=(\ln212)/(\ln(5)) \end{gathered}`

Thus, there is an error in the solution.

CORRECT OPTION: B