Exponential and Logarithmic Equations

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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?

Apr 20th, 2015

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.



Apr 20th, 2015

okay I got to that point without using the calculator. Now its wanting me to substitute (-7/3) for x.

 so log base of 3 (-7/3 -7) - log base of 3 (-7/3) = log base of 3 (4). but it is wanting decimal answers for all the ( ) and that is where I don't know how to but the base in the calculator

Apr 20th, 2015

never mind I have figured it out, thank you anyway

Apr 20th, 2015

Suppose you want to find log 3 (7) .

base is 3. Number is 7.

Find log7/log 3 to calculate log 3 (7) .


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

Apr 21st, 2015

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