# Stewart – Calculus – 1.6 – Inverse Functions and Logarithms

1. Can two different numbers have the same cube?

2. Find the inverse of the equation

3. Find the inverse of the equation

4. True or false:

is equal to
.

5. Solve.

6. Find the inverse function of

7. What is the inverse of the equation $log _{a}x=y$?

8. Find equivalent equations.

9. Find the equations that correspond to the labels.

10. Find equivalent forms.

11. Use the laws of logarithms to evaluate $log_2{80} - log_2{5}$.

12. Find the equivalent natural log.
$log_e{x}$
13. Find the equivalent equation for ln x = y.

14. Find the equivalent forms.

15. Solve the equation
.

16. Express $\ln a+\frac{1}{2}\ln b$ as a single logarithm.

17. The change of base formula says that
For any positive number $a(a{\neq}1)$, we have $log_a{x}=$.

18. Sketch the graph of the function $y=\ln (x-2)-1$.

19. Find the inverse of $\sin ^{-1}x=y$.

20. Evaluate $\tan (\arcsin \frac{1}{3})$.
No.
False.
1. Re-write the equation:
2. Solve this equation for x:
3. Interchange x and y:
4. So, inverse function is:
ln x
Let , so
Then we can draw a right triangle with angle θ as in the figure

and deduce from the Pythagorean Theorem that the third side has length

This enables us to read from the triangle that

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