solve using a graphing calculator log(base 4)(x+2)-log(base 5)(x-1)=1 e^2x=x+2

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embizze | High School Teacher | (Level 1) Educator Emeritus

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Solve `log_4(x+2)-log_5(x-1)=1` :

We can rewrite using the change of base formula: `log_ba=(ln(a))/(ln(b))`


Now we can graph and look for the intersection:

Using the intersect feature we find the solution to be x=2.

This is easily verifiable: `(ln(4))/(ln(4))-(ln(1))/(ln(5))=1-0=1` as required.

(2) Solve `e^(2x)=x+2`

Again we can graph both functions and find the intersection:

The intersect feature gives `x~~.44754216,y~~2.4475422` and `x~~-1.980974,y~~.01902602`


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