How do you solve ${log}_{5} x + {log}_{3} x = 1$ $log_5x + log_3 x=1$ ?

Question

3202 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-07T08:48:41

$x = 1.9211$ $x=1.9211$

${log}_{5} x + {log}_{3} x = 1$ $log_5x+log_3 x=1$ can be written as

$\frac{log x}{log 5} + \frac{log x}{log 3} = 1$ $logx/log5+logx/log3=1$

or $log 3 log x + log 5 log x = log 3 log 5$ $log3logx+log5logx=log3log5$

or $log x = \frac{log 3 log 5}{log 3 + log 5}$ $logx=(log3log5)/(log3+log5)$

or $x = 10^{\frac{log 3 log 5}{log 15}}$ $x=10^((log3log5)/(log15))$

= $10^{\frac{0.4771 \cdot 0.6990}{1.1761}}$ $10^((0.4771*0.6990)/1.1761)$

= $10^{0.2836}$ $10^0.2836$

= $1.9211$ $1.9211$

How do you solve log5x+log3x=1log_5x + log_3 x=1?