Question

Log raiz de 343 base 49

Answer 1

Lembrando que:

$\rightarrow~\sqrt[b]{a^c}~=~a^{\frac{c}{b}}$

$log_{_{49}}\sqrt{343}=x\\\\\\\sqrt{343}=49^x\\\\\\\left(343\right)^{\frac{1}{2}}=\left(49\right)^{x}\\\\\\\left(7^3\right)^{\frac{1}{2}}=\left(7^2\right)^{x}\\\\\\7^{\,3\,.\,\frac{1}{2}}=7^{\,2\,.\,x}\\\\\\7^{\frac{3}{2}}=7^{\,2x}\\\\\\2x=\frac{3}{2}\\\\\\x=\frac{3}{2\,.\,2}\\\\\\\boxed{x=\frac{3}{4}}$