QuestionSolve the equation .
Studdy Solution
STEP 1
Assumptions1. The base of all logarithms in the equation is.
. The variable x is the same in all parts of the equation.
3. The logarithmic equation is valid for x >0 and x ≠1.
STEP 2
We can use the properties of logarithms to simplify the equation. The property allows us to combine the left side of the equation.
becomes
STEP 3
Since the base of the logarithms on both sides of the equation is the same (base2), we can set the arguments of the logarithms equal to each other.
STEP 4
To solve for x, we first get rid of the fraction by multiplying every term by7.
STEP 5
Next, we rearrange the equation to isolate x. Subtract x from both sides to get
STEP 6
Add to both sides to isolate the term with x
STEP 7
Finally, divide both sides by6 to solve for xSo, the solution to the logarithmic equation is .
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