Solve the exponential equation e^{4x-5}-7 = 11243. Express the solution se

floymdiT

floymdiT

Answered question

2021-11-07

Solve the exponential equation e4x57=11243. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution.

Answer & Explanation

AGRFTr

AGRFTr

Skilled2021-11-08Added 95 answers

Step 1: To determine
Given:
e4x57=11243
To determine:
The solution in terms of logarithms & in decimal form.
Step 2:Calculation
Since, e4x57=11243 e4x57=11243+7
e4x57=11250
Now, taking natural log on both the sides of equation, we get,
ln(e4x5)=ln(11250)
4x5ln(e)=ln11250
4x5=ln(11250)
x=ln(11250)+54
Hence, x=ln(11250)+54 is the required solution in logarithm form.
Now, ln(11250)=9.3281
So, x=9.3281+54=3.58
Step 3:Conclusion
Hence, x=ln(11250)+54=3.58 is the required solution

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