Fun with letters

Algebra Level pending

The triple of the base and of the exponent of $s^t$ is $r$ . Also, r is the product of $s^t \times u^t$ , with $s>0, \ u>0, \ t \ne 0$ . So $u$ is equal to:

9s^2

27s^2

27s

9s

3s^2

1 solution

Nicolás Díez Andrés
Apr 7, 2020

$(3s)^{3t} = r$ and $r= s^t \times u^t$

$\Rightarrow \ (3s)^{3t} = s^t \times u^t \\ \Rightarrow 3^{3t} \times s^{3t} = u^t \\ \Rightarrow 3^{3t} \times s^{3t} = s^t \times u^t \\ \Rightarrow 3^{3t} \times \dfrac{ s^{3t}}{s^t} = u^t \\ \Rightarrow 3^{3t} \times s^{2t} = u^t \\ \Rightarrow u = \sqrt[t]{ 3^{3t} \times s^{2t}} \\ \Rightarrow u = 3^3 \times s^2 = 27u^2$

Fun with letters

1 solution

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