Exponential Functions - Problem Solving Practice Problems Online

If $3^n = 5$ and $4^m = 8$ , what is the value of $\large 9^{n+m} ?$

Let $f(x) = \left( \dfrac12 \right)^{x-5} - 64,$ and suppose that the graphs of $y = |f(x)|$ and $y=k$ meet in the first quadrant.

Find the number of all the positive integers $k$ that satisfy the above condition.

For all positive integers $n$ , let $\alpha_n$ and $\beta_n$ be the roots of the quadratic equation $nx^2-x+n(n+1)=0.$ If $\left(\frac{1}{\alpha_1}+\frac{1}{\beta_1}\right)+\left(\frac{1}{\alpha_2}+\frac{1}{\beta_2}\right)+ \cdots +\left(\frac{1}{\alpha_{7}}+\frac{1}{\beta_{7}}\right)=\frac{p}{q},$ where $p$ and $q$ are coprime positive integers, what is $p+q$ ?

What is the sum of all possible integer values of $x$ such that

$\large (x^2-55x+755)^{(x^2-62x+936 )} =1 ?$

Solve for $x$ :

$3 = 4^x + 5^x + 6^x$

Concept Quizzes

Challenge Quizzes

Exponential Functions - Problem Solving