what is x 5^x=17

Take logs of both sides

log(5^x) = log(17)

Use the property of logarithms that states log(a^b) = b*log(a)

x*log(5) = log(17)

x = log(17)/log(5)

$${\mathtt{x}} = {\frac{{log}_{10}\left({\mathtt{17}}\right)}{{log}_{10}\left({\mathtt{5}}\right)}} \Rightarrow {\mathtt{x}} = {\mathtt{1.760\: \!374\: \!427\: \!722\: \!587\: \!7}}$$

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