ln(5x + 7) = 8
Not looking for an answer, I’m just stuck. Could someone give me the steps to solve this?
just ask ur teacher or math tutor
Sure! To solve for x in the equation ln(5x + 7) = 8, you can follow these steps:
Step 1: Start by isolating the natural logarithm function on one side of the equation. In this case, you can do that by subtracting 8 from both sides. This gives you:
ln(5x + 7) - 8 = 0
Step 2: Next, you need to get rid of the natural logarithm. The inverse function of the natural logarithm is exponentiation with the base e. So, you can rewrite the equation using exponential form as:
e^(ln(5x + 7) - 8) = e^0
Step 3: Simplify the right side of the equation. Since any number raised to the power of 0 is equal to 1, you have:
e^(ln(5x + 7) - 8) = 1
Step 4: Now, you can simplify the left side of the equation using the properties of logarithms. The exponential form cancels out the natural logarithm, leaving you with:
5x + 7 - 8 = 1
Simplify the equation:
5x - 1 = 1
Step 5: Move the constant term to the other side of the equation by adding 1 to both sides:
5x - 1 + 1 = 1 + 1
Simplify the equation:
5x = 2
Step 6: Finally, solve for x by dividing both sides of the equation by 5:
(5x)/5 = 2/5
Simplify the equation:
x = 2/5
And that's it! The solution to the given equation is x = 2/5.
Remark:
e ^ ln ( a ) = a
So:
e^ ln ( 5 x + 7 ) = 5 x + 7
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ln ( 5 x + 7 ) = 8
Cancel logarithms by taking expof both sides.
e^ ln ( 5 x + 7 ) = e ^ 8
5 x + 7 = e ^ 8
Subtract 7 to both sides
5 x + 7 - 7 = e ^ 8 - 7
5 x = e ^ 8 - 7
Divide both sides by 5
x = ( e ^ 8 - 7 ) / 5 = 1 / 5 ( e ^ 8 - 7 )