+118724 How do I solve for x?
(a) log4(3) = log5(x) How do I solve for x?
Use the change of base law
$$\\log_4(3) = log_5(x) \\\\
\dfrac{log_{10}3}{log_{10}4}=\dfrac{log_{10}x}{log_{10}5}\\\\
\dfrac{log_{10}3}{log_{10}4}\times{log_{10}5} =log_{10}x\\\\
10^{log_{10}x}=10^{\frac{log_{10}3}{log_{10}4}\times{log_{10}5}} \\\\
x=10^{\frac{log_{10}3}{log_{10}4}\times{log_{10}5}} \\\\$$
$${{\mathtt{10}}}^{\left({\frac{{log}_{10}\left({\mathtt{3}}\right)}{{log}_{10}\left({\mathtt{4}}\right)}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{5}}\right)\right)} = {\mathtt{3.580\: \!309\: \!929\: \!757\: \!902\: \!4}}$$
+118724 How do I solve for x?
(a) log4(3) = log5(x) How do I solve for x?
Use the change of base law
$$\\log_4(3) = log_5(x) \\\\
\dfrac{log_{10}3}{log_{10}4}=\dfrac{log_{10}x}{log_{10}5}\\\\
\dfrac{log_{10}3}{log_{10}4}\times{log_{10}5} =log_{10}x\\\\
10^{log_{10}x}=10^{\frac{log_{10}3}{log_{10}4}\times{log_{10}5}} \\\\
x=10^{\frac{log_{10}3}{log_{10}4}\times{log_{10}5}} \\\\$$
$${{\mathtt{10}}}^{\left({\frac{{log}_{10}\left({\mathtt{3}}\right)}{{log}_{10}\left({\mathtt{4}}\right)}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{5}}\right)\right)} = {\mathtt{3.580\: \!309\: \!929\: \!757\: \!902\: \!4}}$$
