Respuesta :
The solution 'x' of the expressed logarithmic expression is 17.65.
What exactly is the logarithmic expression?
A logarithmic equation one in which the variable x contains a logarithm.
The variable in an exponential formula is signified by an exponent. To solve exponential equations, first see if both sides of the equation can be presented as powers of the same number. Because unless you can't, start taking the common logarithm of both equation sides and solve the problem using property 7.
- Quotient Rule: ㏒(A/B) = ㏒A - ㏒B
- Product Rule : ㏒A + ㏒B = ㏒(AB)
- Power Rule: n㏒A = ㏒Aⁿ
- Exponent Rule = e∧lnx = x
Now, as per the stated log expression;
3 ln x + ln 5 = 7
Apply the Power Rule on the first term of the given equation;
ln x³ + ln 5 = 7
Now, by the Product Rule, we can re-write the equation in the form;
ln (x³×5) = 7
ln (5x³) = 7
Using the exponent form of the log on both side.
e∧ln (5x³) = e⁷
As, we have the same base for the obtained expression. Use the exponent rule;
(5x³) = e⁷
x³ = e⁷/5
Substitute the value of exponent e = 2.72
x³ = (2.72)⁷/5
x³ = 5507.5
Take cube root on both side;
x = 17.65
Thus, solution for the value of 'x' for expressed logarithmic expression is 17.65.
To know more about the logarithmic expression, here
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