SOLUTION: D1: Let�s combine our knowledge of solving systems and solving logarithmic equations. Solve the system of equations: log yx = 3, this is log with a base of y, then x equals 3. l

Question 948326: D1: Let�s combine our knowledge of solving systems and solving logarithmic equations. Solve the system of equations:
log yx = 3, this is log with a base of y, then x equals 3.
log y (4x) = 5, this is log with a base of y,(4x) equals 5.
I am trying to figure this question out. I need steps involved please.
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Equations are
log(y,x)=3,log(y,(4x))=5
as rendered become the system

The second equation is .
Substitute using the first equation for ;

put into exponential form,

or .
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
...change the base to base

...if log same, then we have
...........eq.1

=>

..............eq.2
system is:
...........eq.1
..............eq.2
since left sides same, right sides must be equal too
...divide by

solutions:
=> or

now find
...........if

...........if

intersection points:
(,)
(,)
(,)
check if all satisfy log
since we need => -this is not solution we can use

and => -this solution we can use
and => -this is not solution we can use either

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