Solve the exponential equation. Round your answer to two decimal places. 1 3 ( 6 x + 4 ) = 1200 \frac { 1 } { 3 } \left( 6 ^ { x + 4 } \right) = 1200 3 1 ( 6 x + 4 ) = 1200 A) x = 0.57 x = 0.57 x = 0.57 B) x = − 0.44 x = - 0.44 x = − 0.44 C) x = 7.87 x = 7.87 x = 7.87 D) x = − 0.66 x = - 0.66 x = − 0.66 E) x = − 2.68 x = - 2.68 x = − 2.68

Question

Solve the exponential equation. Round your answer to two decimal places.   1 3 ( 6 x + 4 )  = 1200 \frac { 1 } { 3 } \left( 6 ^ { x + 4 } \right)  = 1200 3 1 ​ ( 6 x + 4 )  = 1200 A)    x = 0.57 x = 0.57 x = 0.57 B)    x = − 0.44 x = - 0.44 x = − 0.44 C)    x = 7.87 x = 7.87 x = 7.87 D)    x = − 0.66 x = - 0.66 x = − 0.66 E)    x = − 2.68 x = - 2.68 x = − 2.68

Jamiya Mason · Accepted Answer

Final Answer : A, Explanation :   First, multiply both sides by 3 to get rid of the fraction:   6 x + 4 = 3600 6^{x+4} = 3600 6 x + 4 = 3600  . Taking the logarithm of both sides (base 6) gives   x + 4 = log ⁡ 6 3600 x + 4 = \log_6{3600} x + 4 = lo g 6 ​ 3600  . Solving for   x x x   involves calculating the logarithm and subtracting 4. Using a calculator,   log ⁡ 6 3600 ≈ 4.57 \log_6{3600} \approx 4.57 lo g 6 ​ 3600 ≈ 4.57  , so   x ≈ 4.57 − 4 = 0.57 x \approx 4.57 - 4 = 0.57 x ≈ 4.57 − 4 = 0.57  .

Solve the exponential equation. Round your answer to two decimal places. $=1200\frac { 1 } { 3 } \left( 6 ^ { x + 4 } \right) = 1200$

A) $x = 0.57$
B) $x = - 0.44$
C) $x = 7.87$
D) $x = - 0.66$
E) $x = - 2.68$

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