## Logarithms – Step by Step – using the TiNspire CX CAS

Using the Step by Step Equation Solver at www.TiNspireApps.com we can solve – step by step – equations involving Logarithms such as

log(x-2)+log(2x+1)=7

just type it in the top box and view the step by step solution in the bottom box:

Another example using natural logarithm instead of base 10 :

Say we are asked to expand logarithms, we will then use the Algebra Made Easy app at www.tinspireapps.com , go to menu option EXPAND, enter our condensed log expression in the top box to view the expanded version as shown below :

and

Lastly , we are given an expanded logarithmic expression and we are asked to condense. Well, you know what to do: use the Algebra Made Easy app at www.tinspireapps.com , go to menu option CONDENSE , enter our expanded log expression in the top box to view the condensed version as shown below :

## Logarithms using the TiNspire CX

Say we have to logarithm base 6 of the cube root of 3 , here is how we enter it into the TiNspire CX CAS:

Upon pressing ENTER we will see the pretty format and the answer:

Let’s do another example: Logarithm base 6 of 1296 :

Pressing ENTER yields the solution 4 (since 1296 = 6^4) :

Here is exponential equation involving logarithm:

This is how it is entered:

Conveniently, log base 10 and exponential base 10 function cancel to get

Now we solve this function:

Voila.

Lastly, evaluate

We enter as

to get

The reason for that clean answer is using the ln rules as follows:

and lastly

We have to solve the following logarithmic equation:

Enter as

log((r+15)^2,3) = 4 and lastly

solve( log((r+15)^2,3) = 4 , r)

which solves for r using the TiNspire cx .

By hand: log_3_(r+15)^2 = 4 calls for exponentiating both sides using base 3 which yields : (r+15)^2 = 3^4 = 81
Square rooting both sides : r+15 = plus or minus 9
Thus, r = -6 or r = -24 . Plug each into the original equation to verify the correctness.

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