Take the Log of both sides; we have:
[tex]\text{Log 5}^{4x-2}=Log3^{2x+1}[/tex]Thus, we have:
[tex](4x-2)Log5=(2x+1)Log3[/tex]Divide both sides by Log5, we have:
[tex]\frac{(4x-2)\text{Log}5}{\text{Log}5}=\frac{(2x+1)\text{Log}3}{\text{Log}5}[/tex][tex]\begin{gathered} (4x-2)=(2x+1)0.6826 \\ 4x-2=1.3652x+0.6862 \\ 4x-1.3652x=0.6862+2 \\ 2.6348x=2.6862 \\ x=\frac{2.6862}{2.6348} \\ x=1.019 \end{gathered}[/tex]Hence, the value of x is 1.019
