Solve the following exponential equation. Be sure to show all the steps of your work 2^{x-1}=5^{3 x+1}

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Accepted Answer

Step:1 ：Given the exponential equation (2^{x-1}=5^{3 x+1})Step:2 ：Take the natural logarithm (ln) of both sides to bring down the exponents. This gives us (ln(2^{x-1}) = ln(5^{3x+1}))Step:3 ：Using the properties of logarithms, we can simplify this to ((x-1)ln(2) = (3x+1)ln(5))Step:4 ：Solving for x, we get (x = log(10^{1/log(2/125)}))Step:5 ：This is the exact solution in terms of logarithms. However, it might be more useful to compute a numerical approximation of this solution.Step:6 ：Computing the numerical approximation, we get (x = -0.556830072355780)Step:7 ：Final Answer: The solution to the equation (2^{x-1}=5^{3 x+1}) is (x = boxed{-0.556830072355780})

Answer

Step: 1 ：Given the exponential equation (2^{x-1}=5^{3 x+1})Step: 2 ：Take the natural logarithm (ln) of both sides to bring down the exponents. This gives us (ln(2^{x-1}) = ln(5^{3x+1}))Step: 3 ：Using the properties of logarithms, we can simplify this to ((x-1)ln(2) = (3x+1)ln(5))Step: 4 ：Solving for x, we get (x = log(10^{1/log(2/125)}))Step: 5 ：This is the exact solution in terms of logarithms. However, it might be more useful to compute a numerical approximation of this solution.Step: 6 ：Computing the numerical approximation, we get (x = -0.556830072355780)Step: 7 ：Final Answer: The solution to the equation (2^{x-1}=5^{3 x+1}) is (x = boxed{-0.556830072355780})

Solve the following exponential equation. Be sure to show all the steps of your work $2^{x - 1} = 5^{3 x + 1}$

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Popular Problems

Solve the following exponential equation. Be sure to show all the steps of your work 2x−1=53x+1

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Popular Problems

Solve the following exponential equation. Be sure to show all the steps of your work $2^{x - 1} = 5^{3 x + 1}$