SOLUTION: Solve the following equation A) 9 log 5 base x = log x base 5 B) log x/2 base 8 = log x base 2

Algebra.Com
Question 1088005: Solve the following equation
A) 9 log 5 base x = log x base 5
B) log x/2 base 8 = log x base 2
Found 2 solutions by math_helper, ikleyn:
Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!
Solve the following equation
A) 9 log 5 base x = log x base 5
B) log x/2 base 8 = log x base 2
—————————————————————————
A) I don't see how to solve this without using an iterative technique





— Maybe another tutor has a better solution. I would be tempted to iterate the last equation until it is (close enough to) zero.
—————————————————————————
This one is easily solved
B)






——
7/18/17 - I can't believe I overlooked that property, , which is easy enough to derive from the change-of-base calculation. Thanks tutor Ikleyn!


Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
.
Solve the following equation
A) 9 log 5 base x = log x base 5
~~~~~~~~~~~~~~~~~~~~~~~~ 
 = .   (1)


There is the basic property of logarithms   = .

Apply it, and your equation  (1) becomes

 =   ====>

 =   ====>

 =   ====>


====  There are actually TWO solutions:


1)  log(5,(x))}}} =   ====>  x = ,     and


2)  log(5,(x))}}} =   ====>  x = .


Answer.  There are TWO solutions:  x =   and  x = .

Solved.


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".


RELATED QUESTIONS

Help!!! Solve the following equation s: a) 9 log5 base x =log x base 5 B) log x/2... (answered by MathLover1)
solve the equation. log base b (X+3) = log base b (8) - log base b... (answered by lwsshak3)
Solve for x: (A.) (5/2) log(base 4)4 = log(base 4)(2x-3) (B.) Log(base 3)(x+2)-... (answered by stanbon)
log base 2 (x-2)+log base 2(8-x)-log base... (answered by stanbon)
1. Solve the following equations a) log(base 5)x+2 + log(base 5) x-2 - log(base 5)4 =... (answered by mananth)
solve log base 5(x+2) + log base 8(x+4) = log abse 8(2) + log base... (answered by stanbon)
Solve for x: A.) Log(base 3)4 + log(base 3)5 = log(base 3)(4x+5) B.)log(base 7)6... (answered by algebrapro18)
Solve for x: (A.) Log(base 5)7 + log(base 5)8 = log(base 5)(2x-4) (B.) Log(base 3)... (answered by Nate)
Solve: log base 2 (3x+6)- log base 2 (x-5)= log base 2... (answered by Nate)