solve
4(7^(x-2)) = 8
7^(x-2)=2
take the log of each side.
(x-2)log7=log2
now solve for x
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To solve the equation 4(7^(x-2)) = 8, we need to isolate the variable x. Here's how you can do it step by step:
Step 1: Simplify the equation.
Multiply the constant 4 by the exponential term 7^(x-2):
4 * 7^(x-2) = 8
Step 2: Solve for the exponential term.
To get rid of the 4 in front of the exponential term, we need to divide both sides of the equation by 4:
(4 * 7^(x-2))/4 = 8/4
7^(x-2) = 2
Step 3: Solve for x using logarithms.
To solve for x, we can take the logarithm of both sides of the equation. Let's use the logarithm with base 7:
log base 7 (7^(x-2)) = log base 7 (2)
(x-2) * log base 7 (7) = log base 7 (2)
Step 4: Simplify the equation.
Since log base 7 (7) = 1, the equation becomes:
(x-2) * 1 = log base 7 (2)
x - 2 = log base 7 (2)
Step 5: Solve for x.
To isolate x, we add 2 to both sides of the equation:
x - 2 + 2 = log base 7 (2) + 2
x = log base 7 (2) + 2
So, the solution to the equation 4(7^(x-2)) = 8 is x = log base 7 (2) + 2.