Question

Solve the inequality graphically. 6^x<3^x

Answer 1

Create equivalent expressions in the equation that all have equal bases, then solve for  x.

x<0

Let's solve your inequality step-by-step:

6^x<3^x

Let's find the critical points of the inequality.

6^x=3^x

Solve Exponent.

6^x=3^x

log(6^x)=log(3^x) (Take log of both sides)

x*(log(6))=x*(log(3))

x=(log(3)/log(6))*(x)

x=0.613147*x

x=0.613147x (Simplify both sides of the equation)

x−0.613147x=0.613147x−0.613147x (Subtract 0.613147x from both sides)

0.386853x=0

0.386853x/0.386853=0/0.386853  (Divide both sides by 0.386853)

x=0

Critical points:

x=0

Check intervals in between critical points. (Test values in the intervals to see if they work.)

x<0 (Works in original inequality)

x>0 (Doesn't work in original inequality)

Answer:

x<0

Answer 2

The value of the variable x is less than zero.

What is inequality?

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality is given below.

6ˣ < 3ˣ

Taking log on both sides. Then we have

              x log6 < x log3

x log 6 - x log3 < 0

x (log 6 - log 3) < 0

                       x < 0

Then the value of the variable x is less than zero.

The graph is given below.

More about the inequality link is given below.

https://brainly.com/question/19491153

#SPJ2