4 + 5^6x = 8
(a) Find the exact solution of the exponential equation in terms of logarithms.
x =
(b) Use a calculator to find an approximation to the solution rounded to six decimal places.
x =
can any body help me out here please?
4 + 5^6x = 8
I will assume you meant
4 + 5^(6x) = 8
5^(6x) = 4
log both sides and use rules of logs
6x log5 = log4
x = log4/(6log5)
b)
x = appr .143559
Sure! I can help you solve this exponential equation.
(a) To find the exact solution in terms of logarithms, we can start by isolating the exponential term. Here's how:
First, subtract 4 from both sides of the equation:
5^6x = 8 - 4
5^6x = 4
Next, take the logarithm (base 5) on both sides of the equation to remove the exponent:
log base 5 (5^6x) = log base 5 (4)
Now we can use the logarithmic property that states log base b (b^x) = x:
6x = log base 5 (4)
Finally, divide both sides of the equation by 6 to solve for x:
x = (1/6) * log base 5 (4)
This is the exact solution to the exponential equation in terms of logarithms.
(b) To find an approximation to the solution, we can use a calculator. Here's the process:
1. Enter the expression (1/6) * log base 5 (4) into your calculator.
2. Press the equals (=) key to get the result.
3. Round the result to six decimal places as required.
The value you obtain will be an approximation to the solution of the equation.
I hope this helps! Let me know if you have any further questions.