Question

Solve the equation algebraically.

2lnx + 7 = ln(4x) + 10

Round your final answers to two decimal places.

Answer 1

x = 80.34 (2 dp)

Explanation:

`2\ln(x)+7=\ln(4x)+10`

`\implies \ln(x^2)+7=\ln(4x)+10`

`\implies \ln(x^2)-\ln(4x)=10-7`

`\implies \ln\left((x^2)/(4x)\right)=3`

`\implies \ln\left((x)/(4)\right)=3`

`\implies e^{\ln\left((x)/(4)\right)}=e^3`

`\implies (x)/(4)=e^3`

`\implies x=4e^3`

`\implies x=80.34 \textsf{ (2 dp)}`