Isolate Exponential Term: Step Title: Isolate the Exponential Term Concise Step Description: Add 7 to both sides of the equation to isolate the exponential term. Step Calculation: 0 + 7 = 3*2^(x-4), so 7 = 3*2^(x-4) Step Output: 7 = 3*2^(x-4)Divide by Coefficient: Step Title: Divide by the Coefficient of the Exponential Term Concise Step Description: Divide both sides of the equation by 3 to solve for the exponential term. Step Calculation: 7 / 3 = 3*2^(x-4) / 3, so 7/3 = 2^(x-4) Step Output: 7/3 = 2^(x-4)Apply Logarithm: Step Title: Apply the Logarithm Concise Step Description: Apply the logarithm to both sides of the equation to solve for the exponent. Step Calculation: log_2(7/3) = log_2(2^(x-4)), so log_2(7/3) = x - 4 Step Output: log_2(7/3) = x - 4Solve for x: Step Title: Solve for x Concise Step Description: Add 4 to both sides of the equation to solve for x. Step Calculation: log_2(7/3) + 4 = x - 4 + 4, so log_2(7/3) + 4 = x Step Output: x = log_2(7/3) + 4

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$0=3\cdot2^{(x-4)}-7$

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0=3\cdot2^{(x-4)}-7

Isolate Exponential Term: Step Title: Isolate the Exponential Term $\newline$ Concise Step Description: Add $7$ to both sides of the equation to isolate the exponential term. $\newline$ Step Calculation: $0 + 7 = 3 \cdot 2^{(x-4)}$ , so $7 = 3 \cdot 2^{(x-4)}$ $\newline$ Step Output: $7 = 3 \cdot 2^{(x-4)}$
Divide by Coefficient: Step Title: Divide by the Coefficient of the Exponential Term $\newline$ Concise Step Description: Divide both sides of the equation by $3$ to solve for the exponential term. $\newline$ Step Calculation: $\frac{7}{3} = \frac{3\cdot 2^{(x-4)}}{3}$ , so $\frac{7}{3} = 2^{(x-4)}$ $\newline$ Step Output: $\frac{7}{3} = 2^{(x-4)}$
Apply Logarithm: Step Title: Apply the Logarithm $\newline$ Concise Step Description: Apply the logarithm to both sides of the equation to solve for the exponent. $\newline$ Step Calculation: $\log_2(\frac{7}{3}) = \log_2(2^{x-4})$ , so $\log_2(\frac{7}{3}) = x - 4$ $\newline$ Step Output: $\log_2(\frac{7}{3}) = x - 4$
Solve for x: Step Title: Solve for x $\newline$ Concise Step Description: Add $4$ to both sides of the equation to solve for x. $\newline$ Step Calculation: $\log_2(\frac{7}{3}) + 4 = x - 4 + 4$ , so $\log_2(\frac{7}{3}) + 4 = x$ $\newline$ Step Output: $x = \log_2(\frac{7}{3}) + 4$