Number 24 isn't really a word problem. They are asking you to solve the equation 1+ 1.5 ln(x+1)= 10. As always, you solve an equation by "backing out": subtract 1 from both sides to get 1.5 ln(x+1)= 9. Divide both sides by 1.5 to get ln(x+1)= 9/1.5= 6.

Notice that each step has been an "inverse"- the opposite of some operation. Initially, we had 1 added on the left so we do the opposite- subtract 1 from both sides. Then we had 1.5 multiplying the function of x so again we do the opposite- divide both sides by 1.5. Now we have a natural logarithm. What is the "opposite" of that? The exponential! ln(x) and

are "inverse functions":

and

.

Taking the exponential of both sides,

.

Finally, of course, subtract 1 from both sides.

. If you want a decimal (but only approximate) answer, use a calculator.