Question

243^0.2x=81^x+5

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

Answer 1

-20/3

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=
`-(20)/(3)`