Find the exact solution of the exponential equation in terms of logarithms.e7 − 8x = 18

Question

Given equation:
$e^7 - 8x = 18$

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Sure, here are the steps to solve the equation e^(7 - 8x) = 18:

Step 1: Take the natural logarithm (ln) on both sides of the equation to get rid of the base e on the left side. This gives us:

7 - 8x = ln(18)

Step 2: Isolate the term with x by subtracting 7 from both sides:

-8x = ln(18) - 7

Step 3: Finally, solve for x by dividing both sides by -8:

x = (ln(18) - 7) / -8

So, the exact solution of the exponential equation in terms of logarithms is x = (ln(18) - 7) / -8.

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