Exponential equations are equations in which variable expressions occur as exponents.
Which equation is different? 3^4=x+4^2 Explanation: See solution.
Practice makes perfect
We are given the equations shown below and asked to find the one that is different.
c|c
2^x = 4^x +6 & 5^(3x+8)=5^(2x)
3^4=x+4^2 & 2^(x-7)=2^7
Note that all of these equations are similar in the sense that they involve powers. We can start by checking which of these are exponential equations. Recall that if a equation contains variable expressions as exponents, then it is an exponential equation. Let's have a second look at the given equations.
c|c
2^x = 4^x +6 & 5^(3x+8)=5^(2x)
3^4=x+4^2 & 2^(x-7)=2^7
Notice that all of them have variable expressions as exponents except for 3^4=x+4^2. We can even calculate the powers to simplify it.
3^4=x+4^2 ⇔ 81 =x+ 16
As we can see, this in fact a linear equation. Therefore, this is the odd one out.
