The t is not in the exponent, so just divide each side by -0.00236.
Answer
t ≈ -274.499
Example 2
Solve 2 log3 (x + 1) = 6.
Hint
Divide each side by 2, then raise each side to an exponent with a base of 3.
Answer
x = 26
Example 3
Solve log3 2x =10.
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.
Answer
x = 29524.5
Example 4
Solve 2x – 1 = 15.
Hint
Take the natural log with each side. Then bring the x – 1 to the front of 2x – 1. You can then divide each side by ln2 and solve for x.
Answer
x ≈ 4.907
Example 5
Solve .
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 .
Answer
x ≈ 0.631
Example 6
Solve .
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.
Answer
x ≈ -4.644
Example 7
Solve log x2 = 4.
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.
Answer
x = 100
Example 8
Solve .
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!
.
.
and divide each side by 
.
.
on the left side of your equation on the last step, so all you need to do is multiply each side by 2.
.
, 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!