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![Log_{ \sqrt{7}}343 =x\\\\ 343 = (\sqrt{7})^x \\
7^3=[(7^{1/2})]^x\\
7^3=7^{{x/2}\\
3 = x/2\\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~\boxed {\boxed{x=6}}](https://tex.z-dn.net/?f=Log_%7B+%5Csqrt%7B7%7D%7D343+%3Dx%5C%5C%5C%5C+343+%3D+%28%5Csqrt%7B7%7D%29%5Ex+%5C%5C+%0A7%5E3%3D%5B%287%5E%7B1%2F2%7D%29%5D%5Ex%5C%5C+%0A7%5E3%3D7%5E%7B%7Bx%2F2%7D%5C%5C%0A+3+%3D+x%2F2%5C%5C%5C%5C+%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%5Cboxed+%7B%5Cboxed%7Bx%3D6%7D%7D "Log_{ \sqrt{7}}343 =x\\\\ 343 = (\sqrt{7})^x \\
7^3=[(7^{1/2})]^x\\
7^3=7^{{x/2}\\
3 = x/2\\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~\boxed {\boxed{x=6}}")
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