Solve In(5x+7) = 8. Round to the nearest thousandth.
Can someone walk me through this?
ln(5x+7) = 8
5x+7 = e^8
5x = e^8 - 7
x = (e^7 - 7)/5
just recall that ^ and log (or ln) are inverse operations, just like
+ and -
* and /
√ and ^2
...
5x+7=e8
Subtract 7 from both sides of the equation.
5x=e8−7
Divide each term by 5 and simplify.
x=e85−75
594.79159740
Thank you, but it's an equation dealing with natural logarithms.
(the “/“ is division)
Sure! To solve the equation ln(5x+7) = 8, we need to isolate the variable x. Here's a step-by-step guide on how to do that:
Step 1: Start by taking the exponential of both sides of the equation in order to cancel out the natural logarithm. Since the exponential function that cancels out ln is e^x, we have:
e^(ln(5x+7)) = e^8
Step 2: Simplify the left side of the equation. The exponential function and the natural logarithm are inverse functions, so they cancel each other out. This leaves us with:
5x+7 = e^8
Step 3: Now, we need to isolate the variable x. Start by subtracting 7 from both sides of the equation:
5x = e^8 - 7
Step 4: Finally, divide both sides of the equation by 5 to solve for x:
x = (e^8 - 7) / 5
Now, to round the solution to the nearest thousandth, you would use a calculator to calculate the value of (e^8 - 7) / 5 and then round the result to three decimal places.
potato
i hope this helps
no parenthesis are needed.
5x+7=8
I would take the 7 and subtract is from 7 and 8
the new equation would look like this
5x= 1
then you would take 5/5 and 1/5 and then there’s your answer. I’m not the greatest at math but this is how I’d do it :)