Exponential Equations

Exponential Equations Exponential equations are basically the tool which is helpful in evaluating the values of unknown variables which are generally in powers. This tool is helpful in evaluating the exponential equations either by comparison method or by taking the logarithmic function in both sides of the equation. This tool eases the calculation steps and hence it easily evaluates the value of unknown variable in exponent or we can say in power. The above concept can be better clarified by taking the suitable examples and the examples are shown below. In this case, for better understanding we will take both the cases that is one of comparison in case of same base and logarithmic method in case of different base. Question 1:- Find x if 3^ (4x) = 27^ (x+1) Solution 1:- Given 3^ (4x) = 27 ^ (x+1) This further implies, 3 ^ (4x) = 3^ (3x+3) Since bases are equal on both sides, it means that its power must also be same. Therefore, 4x = 3x + 3 On solving, we get 4x 3x = 3 Hence x = 3 Question 2:- Find x if 5^x = 10 Solution 2:-Given 5^ x = 10 Since bases are not same, so in this case we need to apply log both sides, Therefore log 5^x = log 10 So x log 5 = log 10 Therefore, x = log 10/log5 By writing down the values of log 10 and log 5, we can easily evaluate the actual value of x.

Seek First to Understand... - Heart Math Tutoring

Seek First to Understand... - Heart Math Tutoring Seek First to Understand Seek First to Understand November 29, 2018 Seek First to Understand… InStephen Coveys“The 7 Habits of Highly Effective People”, Habit #5 is Seek First to Understand, Then to Be Understood. Heart Tutorings Program team recently spent the weekly training time seeking to understand more about our students, most of whom are growing up in various levels of poverty. “Locate a resilient kid and you will also find a caring adultâ€"or severalâ€"who has guided them.”- Invincible Kids, U.S. News World Report “School is the single context within which the combination of skill and relationship development occurs on a regular basis.”- Adolescents at School, Sadowski, 2008 We discussed the quotes above and the role relationships play in learning and the importance of the one-on-one relationships Heart volunteers create. Deposits and Withdrawals Drawing from Ruby Paynes book, “A Framework for Understanding Poverty”, we talked about the long-term impact of relationships. It is critical that those relationships are built on emotional deposits and that emotional withdrawals are avoided. Deposits include seeking first to understand, keeping promises, kindness, courtesies, clarifying expectations, apologies, and openness to feedback. Withdrawals would include seeking first to be understood, unkindness, violating expectations, and rejecting feedback. Heart Tutoring volunteers have plenty of opportunities to make deposits in our students! Every day, we see tutors thanking students for working with them (courtesies), explaining changes in schedule (clarifying expectations), showing up as promised, and taking interest in our students’ day/week/life (kindness). Final Thought: Relationships Count When students who have been in poverty (and have successfully made it into the middle class) are asked how they madethe journey, the answer nine times out of ten has to do with a relationshipâ€"teacher, counselor, or coach who made a suggestion or took an interest in them as individuals.” Excerpt from A Framework for Understanding Poverty by Ruby Payne, 2005