Exponential and Logarithmic Functions Exercises

Hint

The t is not in the exponent, so just divide each side by -0.00236.

Hint

Divide each side by 2, then raise each side to an exponent with a base of 3.

Hint

Raise each side to an exponent with a base of 3 which will cause the left side of the equation to be 2x. Then, solve for x.

Hint

Take the natural log with each side. Then bring the x – 1 to the front of 2^{x – 1}. You can then divide each side by ln2 and solve for x.

Hint

First divide each side by 10. Then take the natural log of both sides. On the right side of the equation, bring the t in front of  and divide each side by .

Hint

First divide each side by 3, then take the natural log of each side. Then, solve for x. You will have  on the left side of your equation on the last step, so all you need to do is multiply each side by 2.

Hint

Since it is a common logarithm (base 10), raise each side of the equation to an exponent using a base of 10. You will be left with x² = 10000, take the square root and you're done! The answer will be positive because we can only have positive values of x.

Hint

Since we have an exponential problem with a base of , we can do the opposite by squaring each side. That will leave you with  on the left and 100 on the right. Keep going, you are almost done!