Question

$e^{4x-5} -7 = 11, 243$

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution.

Answer 1

Answer:

• x = 3.58

Step-by-step explanation:

• $e^{4x - 5}$ - 7 = 11243
• $e^{4x - 5}$ = 11250
• ln $e^{4x - 5}$ = ln 11250
• 4x - 5 = ln 11250
• 4x - 5 = 9.33 (rounded)
• 4x = 14.33
• x = 14.33 / 4
• x = 3.58 (rounded)

Answer 2

Answer:

x = 3.58 (2 d.p.)

Step-by-step explanation:

Given equation:

$e^{4x-5}-7=11243$

Add 7 to both sides:

$\implies e^{4x-5}-7+7=11243+7$

$\implies e^{4x-5}=11250$

Take natural logs of both sides:

$\implies \ln e^{4x-5}=\ln 11250$

$\textsf{Apply the power law}: \quad \ln x^n=n \ln x$

$\implies (4x-5)\ln e=\ln 11250$

As ln(e) = 1:

$\implies 4x-5=\ln 11250$

Add 5 to both sides:

$\implies 4x-5+5=\ln(11250)+5$

$\implies 4x=\ln(11250)+5$

Divide both sides by 4:

$\implies \dfrac{4x}{4}=\dfrac{\ln(11250)+5}{4}$

$\implies x=\dfrac{\ln(11250)+5}{4}$

Using a calculator:

$\implies x=3.582030852...$

Therefore:

$\implies x=3.58\:\: \sf (2 \: d.p.)$

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