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02.03.2022

Solve the equation algebraically. 2lnx + 7 = ln(4x) + 10

Round your final answers to two decimal places.

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09.07.2023, solved by verified expert

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x = 80.34 (2 dp)

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Mathematics

Solve the equation algebraically. 2lnx + 7 = ln(4x) + 10 Round your final answers to two decimal places.

Step-by-step answer

P Answered by Master

x = 80.34 (2 dp)

Step-by-step explanation:

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

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

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

$\implies \ln\left(\dfrac{x^2}{4x}\right)=3$

$\implies \ln\left(\dfrac{x}{4}\right)=3$

$\implies e^{\ln\left(\dfrac{x}{4}\right)}=e^3$

$\implies \dfrac{x}{4}=e^3$

$\implies x=4e^3$

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

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Solve the equation algebraically. 2lnx + 7 = ln(4x) + 10 Round your final answers to two decimal places.

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Solve the equation algebraically. 2lnx + 7 = ln(4x) + 10

Round your final answers to two decimal places.