Exponential and Logarithmic Equations

User Generated

xevfgv0001

Mathematics

Description

log3 (x-7) -log3 (x) = log3 (4)

answer is -7/3

but it is asking to me to substitute the -7/3 in for x in which I did but its wanting a decimal answer for each ( ) I don't know how to put the log base of 3 into my TI 83 calculator to get the correct answer. can you please help me?

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Explanation & Answer

You don't have to use the calculator at all....

Here the base is 3.

log3 (x-7)  -log3 (x) = log3 (4) 

log {(x-7)/3} = log3 (4)   Hint:  log a -log b =log (a/b)

Since the bases are equal, we can equate the x variables and constants in the equation

so (x-7)/x = 4

 x-7 =4x

-7= 4x-x

-7 =3x

x =-7/3

Please let me know if you have any other questions and best me if you are satisfactory.




Anonymous
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