$$(\frac{2}{7})^{-5}\times(\frac{2}{7})^{m}=(\frac{2}{7})^{6}$$
$m=11$
$$\frac{16807}{32}\times \left(\frac{2}{7}\right)^{m}=\frac{64}{117649}$$
$$\left(\frac{2}{7}\right)^{m}=\frac{2048}{1977326743}$$
$$\log(\left(\frac{2}{7}\right)^{m})=\log(\frac{2048}{1977326743})$$
$$m\log(\frac{2}{7})=\log(\frac{2048}{1977326743})$$
$$m=\frac{\log(\frac{2048}{1977326743})}{\log(\frac{2}{7})}$$
$$m=\log_{\frac{2}{7}}\left(\frac{2048}{1977326743}\right)$$
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