QuestionSolve . The solution, to the nearest tenth, is
Studdy Solution
STEP 1
1. The equation involves exponential terms with different bases.
2. We will use logarithms to solve for .
STEP 2
1. Take the logarithm of both sides of the equation.
2. Apply logarithmic properties to simplify the equation.
3. Solve for .
STEP 3
Take the natural logarithm (or common logarithm) of both sides of the equation to bring the exponents down:
STEP 4
Apply the properties of logarithms. First, use the power rule and the product rule :
STEP 5
Rearrange the equation to isolate terms involving :
Combine like terms:
Factor out from the left side:
Solve for :
STEP 6
Calculate the value of using a calculator:
The solution, to the nearest tenth, is:
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