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melisa1 [442]
3 years ago
5

Solve the equation. Round to the nearest hundredth. Show work.

Mathematics
1 answer:
Burka [1]3 years ago
3 0

Answer:

x=-0.75

Step-by-step explanation:

The given equation is

4^{-5x-7}=6^{2x-1}

We take logarithm of both sides to base 10.

\log(4^{-5x-7})=\log(6^{2x-1})

(-5x-7)\log(4)=(2x-1)\log(6)

We expand the brackets to get;

-5x\log(4)-7\log(4)=2x\log(6)-\log(6)

Group similar terms;

-7\log(4)+\log(6)=2x\log(6)+5x\log(4)

-7\log(4)+\log(6)=(2\log(6)+5\log(4))x

\frac{-7\log(4)+\log(6)}{(2\log(6)+5\log(4))}=x

x=-0.752478

To the nearest hundredth.

x=-0.75

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