SOLUTION: Log_64(4^4)=x+1

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Question 1110895: Log_64(4^4)=x+1
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39847) About Me  (Show Source):
You can put this solution on YOUR website!
log%2864%2C4%5E4%29=x%2B1
-
4%2Alog%2864%2C4%29=x%2B1
x=4%2Alog%2864%2C4%29-1

CHANGE OF BASE FORMULA - CHOOSING BASE 2
x=4%28log%282%2C4%29%2Flog%282%2C64%29%29-1
x=4%28log%282%2C2%5E2%29%2Flog%282%2C2%5E4%29%29-1-------step is mistake. exponent 4 should be exponent 6.
.
.

The rest of this is wrong:
x=2-1
highlight%28x=1%29

Answer by ikleyn(54060) About Me  (Show Source):
You can put this solution on YOUR website!
.
log%2864%2C%284%5E4%29%29 = 4%2Alog%2864%2C%284%29%29 = 4%2A%281%2Flog%284%2C%2864%29%29%29 = 4%2A%281%2F3%29 = 4%2F3.



Therefore, the given equation takes the form



4%2F3 = x + 1   and  has the solution  x = 4%2F3-1 = 1%2F3.

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On logarithms and their properties,  see the lessons
    - WHAT IS the logarithm
    - Properties of the logarithm
    - Change of Base Formula for logarithms
    - Solving logarithmic equations
    - Using logarithms to solve real world problems
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Logarithms".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.


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Be aware:   The solution by  @josgarithmetic  and his answer  x = 1   are   W R O N G.


Answer by MathTherapy(10895) About Me  (Show Source):
You can put this solution on YOUR website!
Log_64(4^4)=x+1
*************
log+%2864%2C+%284%5E4%29%29+=+x+%2B+1
    64%5E%28x+%2B+1%29+=+4%5E4 ---- Converting to EXPONENTIAL form
%284%5E3%29%5E%28x+%2B+1%29+=+4%5E4
   4%5E%283x+%2B+3%29+=+4%5E4
       3x + 3 = 4 ----- Equating EXPONENTS, since bases are equal
              3x = 4 - 3
              3x = 1___highlight%28x+=+1%2F3%29