Final answer:
The given mathematical problem can be solved by simplifying the equation, taking the logarithm base 18 on both sides to deal with the exponential factor and then solving for 'r'. Remember to round your answer to the nearest ten-thousandth.
Step-by-step explanation:
To solve the equation 2*18^(7-7r)+5=24, you first eliminate the coefficient of 2 and the constant of 5. This gives us 18^(7-7r) = 9.5.
We recognize that this is an exponential equation where the base is 18 and the exponent is a linear function of r. Therefore, we can solve this equation by taking the logarithm to the base of 18 on both sides. This transforms our equation to 7 - 7r = log189.5.
Now, isolate r , which will lead to r = (7 - log189.5) / -7. Once we calculate this value, we then round it to the nearest ten-thousandth as asked.
Please remember when using a calculator to set it to the right base(18) logarithm.
Learn more about Solving exponential equations