Answer:
-20/3
Step-by-step explanation:
First simplify the left side of the equation
243^(1/5x)= (243^1/5)^x
=([tex]\sqrt[5]{243}[/tex] )^x
= 3^x
Now that the left side is simplified, let's move to the right side
81^(x+5)=( [tex]3^{4}[/tex])^(x+5) simplify 81 to base 3^4
=[tex]x^{4(x+5)[/tex] use the product of powers property to multiply the exponents together
=[tex]x^{4x+20[/tex]
With both sides simplified, let's rewrite the equation, this time in simplified terms
[tex]3^{x}[/tex]=[tex]3^{4x+20}[/tex]
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=[tex]-\frac{20}{3}[/tex]
