Solve Exponential Equations

An exponential equation is an equation in which a variable appears in the exponent. For example, $$2^x = 8$$ .

First, rewrite 4 as $$2^2$$ , so the equation becomes $$2^x = (2^2)^{x+1}$$ . Then, simplify to $$2^x = 2^{2x + 2}$$ . Set the exponents equal: $$x = 2x + 2$$ , leading to $$x = -2$$ .

Isolate the exponential part by dividing both sides by 2, resulting in $$(3)^k = 81$$ .

The exponential form of 6 is $$6^1$$ .

Multiply both sides by 2 to isolate the exponential part, resulting in $$(7)^x = 343$$ .

Rewrite 8 as $$2^3$$ , so $$2^3 = 2^{5x + 7}$$ . Set the exponents equal: $$3 = 5x + 7$$ , leading to $$x = -\frac{4}{5}$$ .

The base is the constant that is raised to a power. In $$2^x$$ , the base is 2.

To isolate the exponential part means to manipulate the equation so that the exponential expression is alone on one side of the equation.

Rewrite 27 as $$3^3$$ , so $$3^x = 3^3$$ . Therefore, $$x = 3$$ .

The exponential form is $$x = 4$$ or $$x = -4$$ .