Question

Solve the following equation giving answer to 3 decimal places.5^4x-2 = 3^2x+1

Answer 1

`5^(4x-2)=3^(2x+1)`

Take the Log of both sides; we have:

`\text{Log 5}^(4x-2)=Log3^(2x+1)`

Thus, we have:

`(4x-2)Log5=(2x+1)Log3`

Divide both sides by Log5, we have:

`\frac{(4x-2)\text{Log}5}{\text{Log}5}=\frac{(2x+1)\text{Log}3}{\text{Log}5}`
`\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=(2.6862)/(2.6348) \\ x=1.019 \end{gathered}`

Hence, the value of x is 1.019