Use the power rule for logarithms to solve an equation containing the variable in an exponent Sometimes the variable of interest in an equation is contained within an exponent. For example, say we’d like to solve for [latex]x[/latex] in the equation [latex]3^{x}=17[/latex].

How to solve equations with variables in the exponent, power point plus practice problems explained step by step.

Demonstrates how to solve exponential equations by using logarithms. Explains how to recognize when logarithms are necessary. Provides worked examples showing how to obtain "exact" answers.

2024年9月17日 · Solving exponential equations involves isolating the variable in the exponent and often requires taking the logarithm of both the sides of the equation. An exponential function is a mathematical expression in which a constant base is raised to the variable exponent. It can be written as: f (x) = ax.

Step 1: Isolate the exponential and then apply the logarithm to both sides. Step 2: Apply the power rule for logarithms and write the exponent as a factor of the base. Step 3: Solve the resulting equation.

2024年8月4日 · How to Solve Exponential Equations. Boil everything down to a single base-to-a-power term on one side of the equals. Take the (appropriate) log of both sides and use the bring-powers-down Log Law. At this point, no variables should be stuck upstairs anymore. Solve for the variable as usual. Check your answer(s) by plugging back in. There may or ...

2021年10月6日 · Sometimes we will be asked to solve for the unknown variable in an exponential equation. There are two main ways of solving for this type of equation and we’ll go over each type below. (Method 1) Same Base (Method 2) Different Base. Let’s dive right in and look at three different examples applying one of the two methods above.

How to solve exponential equations with different bases? When it’s not convenient to rewrite each side of an exponential equation so that it has the same base, you do the following: Take the log (or ln) of both sides; Apply power property; Solve for the variable; Example: Solve for x. a) 6 x = 42 b) 7 x = 20 c) 8 2x - 5 = 5 x + 1 d) 3 x = 5 x ...

2011年3月24日 · In this tutorial I will walk you through how to solve equations that have exponential expressions. In these equations, you will notice that the variable that we are solving for is in the exponent. We are use to seeing the variable in the base.