Algebra 2 Practice - Solving Exponential Equations Using Logarithms (Example 3)

Please subscribe!    / nickperich   *Algebra 2 Practice - Solving Exponential Equations Using Logarithms (Example 1)* In this type of problem, you are given an equation where the variable is in the exponent, and you solve for the variable using logarithms. *Example 1: Solve for \( x \)* \[ 5^x = 20 \] *Steps:* 1. *Take the natural logarithm (ln) or common logarithm (log) on both sides* \[ \ln(5^x) = \ln(20) \] (You can also use log base 10: \( \log(5^x) = \log(20) \)) 2. *Apply the logarithm power rule* \[ x \ln(5) = \ln(20) \] (Using \( \ln(a^b) = b \ln(a) \)) 3. *Solve for \( x \)* \[ x = \frac{\ln(20)}{\ln(5)} \] 4. *Calculate the value using a calculator* \[ x \approx \frac{2.9957}{1.6094} \approx 1.86 \] *Final Answer:* \[ x \approx 1.86 \] This means \( 5^{1.86} \approx 20 \), confirming the solution. I have many informative videos for Pre-Algebra, Algebra 1, Algebra 2, Geometry, Pre-Calculus, and Calculus. Please check it out: / nickperich Nick Perich Norristown Area High School Norristown Area School District Norristown, Pa #math #algebra #algebra2 #maths #math #shorts #funny #help #onlineclasses #onlinelearning #online #study