  # How To Solve For X In Exponential Equations

How To Solve For X In Exponential Equations. Applying the property of equality of exponential function, the equation can be rewrite as follows: A x = a y, a ≠ 1 a x a y = 1 a x − y = 1 x − y = 0 x = y.

A) log 3 5 + log 2 (x + 4) = 2 b) log 4 x + log 4 (x + 3) = 1; This is easier than it looks. A x = a y, a ≠ 1 a x a y = 1 a x − y = 1 x − y = 0 x = y.

### Log A A G(X) = G(X) Examples:

$x^{n}x^{m}=x^{n+m}$ $x^{n}y^{n}=(xy)^{n}$ now taking the following example with the above power and exponent formula: You have two to the 3x plus five power, and then you have 64 to the x minus seven. Hence, the equation indicates that x is equal to 1.

### Step 1:Take The Natural Log Of Both Sides:

Log 2 4x + log 2 x = 2; In solving exponential equations, the following theorem is often useful: Solve the linear equation as you normally would.

### X= Ln(30)/Ln(2) Either Way, I Get The Same Answer, But Taking Natural Log In The First Place Was Simpler And Shorter.

An exponential equation is an equation in which a variable occurs as an exponent. If you graph an exponential function (this i will explain in another section) you will get a graph looking similar to the one on the picture next to this text. Use exponents laws to simplify.

### Example 1:Solve For X In The Equation.

Applying the property of equality of exponential function, the equation can be rewrite as follows: Rule of the equation denoted that where the bases are the same, the exponent should be equal. So, write a new equation that sets the exponents equal to each other.

Step 2:simplify the left side of the above equation using logarithmic rule 3: Let us first make the substitution $x = e^t$. To solve exponential equations, the following are the most important formulas that can be used to multiply the exponents together.