Question Number 146895 by mathdanisur last updated on 16/Jul/21
$$\frac{\mathrm{1}}{\mathrm{2}\:+\:\boldsymbol{{log}}_{\mathrm{3}} \left(\mathrm{25}\right)}\:+\:\frac{\mathrm{1}}{\mathrm{2}\:+\:\boldsymbol{{log}}_{\mathrm{5}} \left(\mathrm{9}\right)}\:=\:? \\ $$
Answered by EDWIN88 last updated on 16/Jul/21
$$\Rightarrow\:\mathrm{L}\:=\frac{\mathrm{1}}{\mathrm{2}+\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{25}\right)}+\frac{\mathrm{1}}{\mathrm{2}+\mathrm{log}\:_{\mathrm{5}} \left(\mathrm{9}\right)} \\ $$$$\Rightarrow\mathrm{L}=\frac{\mathrm{1}}{\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{9}×\mathrm{25}\right)}\:+\frac{\mathrm{1}}{\mathrm{log}\:_{\mathrm{5}} \left(\mathrm{9}×\mathrm{25}\right)} \\ $$$$\Rightarrow\mathrm{L}=\mathrm{log}\:_{\mathrm{225}} \left(\mathrm{3}\right)+\mathrm{log}\:_{\mathrm{225}} \left(\mathrm{5}\right) \\ $$$$\Rightarrow\mathrm{L}=\mathrm{log}\:_{\mathrm{225}} \left(\mathrm{15}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$
Commented by mathdanisur last updated on 16/Jul/21
$${thank}\:{you}\:{Ser} \\ $$