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Chapter 11: Q. 53 (page 773)

In Problems 25-54, solve each system. Use any method you wish.

lnx=4lnylog3x=2+2log3y

Short Answer

Expert verified

The solution forlnx=4lnylog3x=2+2log3yis,81,3.

Step by step solution

01

Step 1 Given that, 

lnx=4lnylog3x=2+2log3y

Consider the first equation,

lnx=4lny

we can rewrite it as,

lnx=lny4x=y4

We know that,log39=2.

Substitute the known value in the second equation.

log3x=log39+2log3y.

02

Step 2 Now simplify it.

log3x-log39+2log3y=0log3x-log39+log3y2=0

Now combine the second and third term of the equation and also replace 0with log31.

log3x-log39y2=log31log3x9y2=log31x9y2=1x=9y2

03

Step 3 Now equate x=y4 and x=9y2.

y4=9y2y4y2=9y2y2y2=9y=卤3

Since the logarithm of a negative value cannot be defined, y鈮�-3.

So, y=3.

04

Step 4 We know that, x=y4.

So, x=34

x=81

The solution for the given system of equations is,81,3.

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