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Solve For X:


4^-5x=15^(-x+6)


Find an exact answer using the common (base -10) logarithm

A - x=(6 log 15)/(log 15+5 log 4)

B - x=(log 15 -5 log 4)/(6 log 15)

C - x=(log 15 + 5 log 4)/(6 log 15)

D - x=(6 log 15)/(log 15 -5 log 4)

Answer :

abidemiokin

The exact answer using the common (base -10) logarithm is x =  6log15/-5log4+log15

Solving logarithmic expression

Given the expression below;

4^-5x=15^(-x+6)

We are to find the value of x as shown below;

Given

4^-5x=15^(-x+6)

Take the log of both sides

log(4^-5x) = log[15^(-x+6)]

-5xlog4 =  (-x+6)log15

Expand

-5xlog4 = -xlog15 + 6 log15

Collect the like terms

-5xlog4 + xlog15 = 6log15

x (-5log4+log15) =  6log15

x =  6log15/-5log4+log15

Hence the exact answer using the common (base -10) logarithm is x =  6log15/-5log4+log15

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