Expand menu menu_open Minimize Start chapters Home History history History expand_more
{{ item.displayTitle }}
navigate_next
No history yet!
Progress & Statistics equalizer Progress expand_more
Student
navigate_next
Teacher
navigate_next
{{ filterOption.label }}
{{ item.displayTitle }}
{{ item.subject.displayTitle }}
arrow_forward
No results
{{ searchError }}
search
menu_open
{{ courseTrack.displayTitle }}
{{ statistics.percent }}% Sign in to view progress
{{ printedBook.courseTrack.name }} {{ printedBook.name }}
search Use offline Tools apps
Login account_circle menu_open

Solving Exponential Equations

Solving Exponential Equations 1.7 - Solution

arrow_back Return to Solving Exponential Equations
To solve the given exponential equation, we will start by rewriting the terms so that they have a common base.
84x+2=648^{4x+2}=64
84x+2=828^{4x+2}=8^2
Now, we have two equivalent expressions with the same base. If both sides of the equation are equal, the exponents must also be equal. 84x+2=824x+2=2\begin{gathered} 8^{{\color{#0000FF}{4x+2}}}=8^{{\color{#0000FF}{2}}} \quad \Leftrightarrow \quad {\color{#0000FF}{4x+2}}={\color{#0000FF}{2}} \end{gathered} Finally, we will solve the equation 4x+2=2.4x+2=2.
4x+2=24x+2=2
4x=04x=0
x=0x=0