243^0.2x=81^x+5

Could you please help me with the steps to this problem?​

-20/3

Step-by-step explanation:

First simplify the left side of the equation

243^(1/5x)= (243^1/5)^x

                =( )^x

                = 3^x

Now that the left side is simplified,  let's move to the right side

81^(x+5)=( )^(x+5) simplify 81 to base 3^4

             = use the product of powers property to multiply the exponents together

             =

With both sides simplified, let's rewrite the equation, this time in simplified terms

=            

x=4x+20    because both the bases are same, their exponential value must also be equal

-3x=20 solve the algebraic equation for x

  x=

d

step-by-step explanation:

d

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3