Having a really hard time with this!
e^8x^2-5 = 14
solve the exponential equation express in exact form.
Someone please help!
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e^8x^2 = 29
x^2 = 29/e^8
x = ± √(29/e^8)
To solve the equation e^8x^2 - 5 = 14, you need to isolate the exponential term e^8x^2 on one side of the equation.
Step 1: Add 5 to both sides of the equation to eliminate the -5 term on the left side:
e^8x^2 = 14 + 5
e^8x^2 = 19
Step 2: To eliminate the exponential term e^8x^2, you can take the natural logarithm (ln) of both sides of the equation. This will allow you to solve for x:
ln(e^8x^2) = ln(19)
8x^2 ln(e) = ln(19)
8x^2 = ln(19)
Step 3: Divide both sides of the equation by 8 to isolate x^2:
x^2 = ln(19) / 8
Step 4: Take the square root of both sides to solve for x:
x = ±sqrt(ln(19) / 8)
Note that the natural logarithm ln is used instead of the base 10 logarithm log because the exponential function e^x has the natural logarithm as its inverse.
Therefore, the solution to the equation e^8x^2 - 5 = 14, expressed in exact form, is x = ±sqrt(ln(19) / 8).