The solution of the given equation. 5(1.3)^{x}+4=104

e1s2kat26

e1s2kat26

Answered question

2021-09-21

The solution of the given equation.
5(1.3)x+4=104

Answer & Explanation

saiyansruleA

saiyansruleA

Skilled2021-09-22Added 110 answers

Concept used: The property of natural logarithmic functions.
Calculation:
51.3+4=104
51.3=1044
51.3=100
1.3x=1005
1.3x=20
Taking natural logarithm of both sides:
ln(1.3x)=ln20
xln1.3=ln20[lnam=mlna]
x=ln20ln1.3
x=2.9957322730.262364264 (Using a scientific calculator)
x=11.418217643
x=11.418 (Rounded to three decimal places)
Conclusion: The equation 5(1.3)x+4=104 has the solution x=11.418.

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