Answer:
[tex]x=-0.75[/tex]
Step-by-step explanation:
The given equation is
[tex]4^{-5x-7}=6^{2x-1}[/tex]
We take logarithm of both sides to base 10.
[tex]\log(4^{-5x-7})=\log(6^{2x-1})[/tex]
[tex](-5x-7)\log(4)=(2x-1)\log(6)[/tex]
We expand the brackets to get;
[tex]-5x\log(4)-7\log(4)=2x\log(6)-\log(6)[/tex]
Group similar terms;
[tex]-7\log(4)+\log(6)=2x\log(6)+5x\log(4)[/tex]
[tex]-7\log(4)+\log(6)=(2\log(6)+5\log(4))x[/tex]
[tex]\frac{-7\log(4)+\log(6)}{(2\log(6)+5\log(4))}=x[/tex]
[tex]x=-0.752478[/tex]
To the nearest hundredth.
[tex]x=-0.75[/tex]
