Question

243^0.2x=81^x+5Could you please help me with the steps to this problem?​

Answer 1

Answer:

-20/3

Step-by-step explanation:

First simplify the left side of the equation

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

                =($\sqrt[5]{243}$ )^x

                = 3^x

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

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

             =$x^{4(x+5)$ use the product of powers property to multiply the exponents together

             =$x^{4x+20$

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

$3^{x}$=$3^{4x+20}$            

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=$-\frac{20}{3}$