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Question Number 75840 by gugum last updated on 18/Dec/19

$$\mathrm{If}{x}^{200}<3^{300},\mathrm{then}\mathrm{greatest}\mathrm{possible}$$ $$\mathrm{integral}\mathrm{value}\mathrm{of}x\mathrm{is}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}.$$

Answered by mr W last updated on 19/Dec/19

$$x^{200}<3^{300}$$ $${\left(x^2\right)}^{100}<{\left(3^3\right)}^{100}$$ $$x^2<3^3=27$$ $$x<\sqrt{27}$$ $$x⩽5$$ $$\Rightarrow x_{max}=5$$

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