calc prerequisites help me please with logarithms n function

[gcfan4life1023]

I do not know where to begin with any of this homework. I amso confused with all the concepts so far that we read about in our textbook.
I dont know how to do numbers 37-40 or even where to begin
Im suppose to solve the equation algebraically Support my solution graphically.
#37- (1.045)^t= 2
#38- e^0.05t= 3
can somebody please explain to me how to do these and problems like these step by step in detail so maybe i can understand
Can somebody please like demonstrate how to solve one of these problems please thanks

 

[stapel]

In general, solving an exponential function requires taking logs of either side, and applying log rules and algebraic manipulations to arrive that the solution. For instance:

. . . . .3^4x = 15

. . . . .ln(3^4x) = ln(15)

. . . . .(4x)(ln(3)) = ln(15)

. . . . .4x = ln(15)/ln(3)

. . . . .x = ln(15)/[4ln(3)]

This would be the "exact" solution, but you could plug it into your calculator to get a decimal approximation as well.

Your examples work the same way.

Eliz.

 

[soroban]

Re: calc prerequisites help me please with logarithms n func

Hello, gcfan4life1023!

You're expected to know the "log rules" . . .

37) .(1.045)^t = 2
.

Take logs of both sides. .(The base doesn't matter, let's use e.)
. . . ln(1.045^t) .= .ln(2)

Then we have:. t·ln(1.045) .= .ln(2)

. . . . . . . . . . . . . . . . ln(2)
Solve for t: . t .= .------------- .= .15.74730184...
. . . . . . . . . . . . . . .ln(1.045)

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Let's check our answer. .Take x = 15.7473

Is it true that: .1.045^15.7473 .= .2 ?

On my calculator: .1.045^15.7473 .= .1.999999838

. . Close enough!