Question

find x such that 3^x+2=3^x + 216

Answer 1

Answer:

X=3 if question is 3^(x+2)=3^x+216

Step-by-step explanation:

Answer 2

The required solution is x=3

Step-by-step explanation:

$3^{x+2} =3^{x} +216\\\\\Rightarrow 3^{x}\times3^{2}=3^{x}+216$

Using Exponential product rule :  $x^{a}\times x^{b}=x^{a+b}$

We will bring the like terms together:

$\Rightarrow 3^{x}\times3^{2}-3^{x}=3^{x}-3^{x}+216\\\\\Rightarrow 3^{x}(3^{2}-1)=216\\\\\Rightarrow 3^{x}(9-1)=216\\\\\Rightarrow 3^{x}(8)=216\\\\\Rightarrow \frac{3^{x}(8)}{8} =\frac{216}{8}\\\\\Rightarrow 3^{x} =27$

Using the property of logarithm $log_aa^{x}=x$

$\Rightarrow x=log_327\\\\\Rightarrow x=log_33^{3} \\\\\Rightarrow x=3$

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13x-5=3/2

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