How do you simplify $5^{{log}_{5} x}$ $5^(log_5x)$ ?

Question

9641 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-13T11:34:15

See below.

Make $y = 5^{{log}_{5} x}$ $y = 5^(log_5x)$

Apply ${log}_{5}$ $log_5$ to both sides

${log}_{5} y = {log}_{5} x {log}_{5} 5 = {log}_{5} x \cdot 1 = {log}_{5} x$ $log_5y=log_5xlog_5 5=log_5x cdot 1=log_5 x$

Now ${log}_{5} y = {log}_{5} x \to y = x$ $log_5y=log_5x->y=x$ so

$5^{{log}_{5} x} = x$ $5^(log_5x)=x$

How do you simplify 5^(log_5x)5log5x5^(log_5x)?