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alex41 [277]
2 years ago
15

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

Mathematics
1 answer:
Natasha_Volkova [10]2 years ago
3 0

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}

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