Find the solution of the exponential equation

in terms of logarithms, or correct to four decimal places.

Ask by Kirk King. in the United States

Mar 15,2025

Question

Find the solution of the exponential equation $$ 14 e^{x}-20=20 $$ in terms of logarithms, or correct to four decimal places. $$ x=\square $$

UpStudy AI · Accepted Answer

Solve the equation $$ 14e^{x}-20=20 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$14e^{x}-20=20$$
- step1: Move the expression to the left side:
  $$14e^{x}-20-20=0$$
- step2: Subtract the numbers:
  $$14e^{x}-40=0$$
- step3: Rewrite the expression:
  $$14e^{x}=40$$
- step4: Divide both sides:
  $$\frac{14e^{x}}{14}=\frac{40}{14}$$
- step5: Divide the numbers:
  $$e^{x}=\frac{20}{7}$$
- step6: Take the logarithm of both sides:
  $$\ln{\left(e^{x}\right)}=\ln{\left(\frac{20}{7}\right)}$$
- step7: Evaluate the logarithm:
  $$x=\ln{\left(\frac{20}{7}\right)}$$
- step8: Transform the expression:
  $$x=\ln{\left(20\right)}-\ln{\left(7\right)}$$
The solution to the exponential equation $$14e^{x}-20=20$$ in terms of logarithms is $$x=\ln(20)-\ln(7)$$. Correct to four decimal places, the solution is approximately $$x\approx 1.0498$$.
$$ x \approx 1.0498 $$

Find the solution of the exponential equation

in terms of logarithms, or correct to four decimal places.

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Find the solution of the exponential equation in terms of logarithms, or correct to four decimal places.