Solve the equation. Give the exact solution.
2*10^(5x-3)+5=17
rearrange the equation
10^(5x-3)=6
take the log base 10 of each side
5x-3=log6
then solve for x
I hope you are not paying for a course in calculus, this is plain algebra II.
To solve the equation 2*10^(5x-3) + 5 = 17, we can start by isolating the term with the exponential expression. We do this by subtracting 5 from both sides of the equation:
2*10^(5x-3) = 17 - 5
2*10^(5x-3) = 12
Next, we can divide both sides of the equation by 2 to isolate the exponential term:
10^(5x-3) = 12/2
10^(5x-3) = 6
Now, to get rid of the exponentiation, we can take the logarithm (base 10) of both sides of the equation:
log(10^(5x-3)) = log(6)
(5x-3) * log(10) = log(6)
Since log(10) is equal to 1, the equation simplifies to:
(5x-3) = log(6)
Finally, we solve for x by adding 3 to both sides of the equation:
5x = log(6) + 3
Dividing both sides of the equation by 5 gives us the exact solution for x:
x = (log(6) + 3) / 5
To solve the equation 2*10^(5x-3) + 5 = 17, we can follow these steps:
Step 1: Subtract 5 from both sides of the equation:
2*10^(5x-3) = 17 - 5
Simplifying,
2*10^(5x-3) = 12
Step 2: Divide both sides by 2:
10^(5x-3) = 12/2
Simplifying,
10^(5x-3) = 6
Step 3: Perform logarithm operation on both sides with base 10 to eliminate the exponential term:
log(10^(5x-3)) = log(6)
This can also be written as,
(5x-3) * log(10) = log(6)
Step 4: Simplify the logarithm terms:
(5x-3) * 1 = log(6)
or,
5x-3 = log(6)
Step 5: Add 3 to both sides to isolate the variable:
5x = log(6) + 3
Step 6: Divide both sides by 5:
x = (log(6) + 3)/5
Therefore, the exact solution to the equation 2*10^(5x-3) + 5 = 17 is:
x = (log(6) + 3)/5