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Question Number 95230 by i jagooll last updated on 24/May/20

$$\underset{x\to 0^{+}}{\lim }\frac{7^{\sqrt{\mathrm{x}}}-1}{2^{\sqrt{\mathrm{x}}}-1}=?$$

Answered by bobhans last updated on 24/May/20

$$\underset{x\to 0^{+}}{\mathrm{li}\stackrel{\mathrm{L}}{\mathrm{m}}}\frac{\frac{1}{2\sqrt{\mathrm{x}}}{7}^{\sqrt{\mathrm{x}}}\ln \left(7\right)}{\frac{1}{2\sqrt{\mathrm{x}}}{2}^{\sqrt{\mathrm{x}}}\ln \left(2\right)}=\frac{\ln \left(7\right)}{\ln \left(2\right)}=\log {}_2\left(7\right)$$

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