Guided Learning Extension
Let's go further with solving equations with logs by using the properties of logs that we learned in Target C.
Example 1: Solve for x: \(\log_53+\log_5x=2\).
\(\begin{align}&\log_53x=2\ & \ \ \ &\text{1) Rewrite the log using the Product Property.}\\
&5^2=3x\ & \ \ \ &\text{2) Rewrite the log in exponential form.}\\
&25=3x \ & \ \ \ &\text{3) Evaluate the exponent.}\\
&x=\frac{25}{3} \ & \ \ \ &\text{4) Divide.}\end{align}\)
Check for extraneous solutions. Remember that for the equation \(\log_by=x\) both \(b\) and \(y\) have to be positive and \(b ≠1\).
Example 2: Solve for \(x\): \(\log_{\left(x+4\right)}\left(x+6\right)=2\).
Let's go further with solving equations with logs by using the properties of logs that we learned in Target C.
Example 1: Solve for x: \(\log_53+\log_5x=2\).
\(\begin{align}&\log_53x=2\ & \ \ \ &\text{1) Rewrite the log using the Product Property.}\\
&5^2=3x\ & \ \ \ &\text{2) Rewrite the log in exponential form.}\\
&25=3x \ & \ \ \ &\text{3) Evaluate the exponent.}\\
&x=\frac{25}{3} \ & \ \ \ &\text{4) Divide.}\end{align}\)
Check for extraneous solutions. Remember that for the equation \(\log_by=x\) both \(b\) and \(y\) have to be positive and \(b ≠1\).
Example 2: Solve for \(x\): \(\log_{\left(x+4\right)}\left(x+6\right)=2\).