How do you expand ${log}_{b} x^{7}$ $log_b x^7$ ?

Question

1936 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-18T09:39:20

${log}_{b} x^{7} = \frac{7 log x}{log b}$ $log_b x^7=(7logx)/logb$

Using the identities ${log}_{b} a^{m} = m {log}_{b} a$ $log_b a^m=mlog_b a$ and ${log}_{b} a = \frac{log a}{log b}$ $log_b a=loga/logb$ ,

${log}_{b} x^{7}$ $log_b x^7$

= $7 {log}_{b} x$ $7log_b x$

= $\frac{7 log x}{log b}$ $(7logx)/logb$

How do you expand logbx7log_b x^7?