Solve the exponential equation. Round your answer to two decimal places. 7 x + 3 − 5 = 18 7 ^ { x + 3 } - 5 = 18 7 x + 3 − 5 = 18 A) x= -0.77B) x = − 1.64 x = - 1.64 x = − 1.64 C) x = − 1.39 x = - 1.39 x = − 1.39 D) x = 3.49 x = 3.49 x = 3.49 E) x = − 0.69 x = - 0.69 x = − 0.69

Question

Solve the exponential equation. Round your answer to two decimal places.   7 x + 3 − 5 = 18 7 ^ { x + 3 } - 5 = 18 7 x + 3 − 5 = 18 A)  x= -0.77B)    x = − 1.64 x = - 1.64 x = − 1.64 C)    x = − 1.39 x = - 1.39 x = − 1.39 D)    x = 3.49 x = 3.49 x = 3.49 E)    x = − 0.69 x = - 0.69 x = − 0.69

Randa Reges · Accepted Answer

Final Answer : C, Explanation :   To solve for x, we can start by isolating the exponential term: 7 x + 3 = 23 7 ^ { x + 3 } = 23 7 x + 3 = 23 Then, take the logarithm of both sides with base 7: ( x + 3 ) log ⁡ 7 ( 7 ) = log ⁡ 7 ( 23 ) (x+3)\log_7(7)=\log_7(23) ( x + 3 ) lo g 7 ​ ( 7 ) = lo g 7 ​ ( 23 ) Simplifying, x + 3 = log ⁡ 7 ( 23 ) log ⁡ 7 ( 7 ) x+3=\frac{\log_7(23)}{\log_7(7)} x + 3 = lo g 7 ​ ( 7 ) lo g 7 ​ ( 23 ) ​ x + 3 = log ⁡ 7 ( 23 ) x+3=\log_{7}(23) x + 3 = lo g 7 ​ ( 23 ) x = log ⁡ 7 ( 23 ) − 3 x=\log_{7}(23)-3 x = lo g 7 ​ ( 23 ) − 3 Using a calculator, we get: x ≈ − 1.39 x\approx -1.39 x ≈ − 1.39 Therefore the answer is C).

Solve the exponential equation. Round your answer to two decimal places. $7 ^ { x + 3 } - 5 = 18$

A) x= -0.77
B) $x = - 1.64$
C) $x = - 1.39$
D) $x = 3.49$
E) $x = - 0.69$

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Solve the exponential equation. Round your answer to two decimal places. 7x+3−5=187 ^ { x + 3 } - 5 = 187x+3−5=18 A) x= -0.77B) x=−1.64x = - 1.64x=−1.64 C) x=−1.39x = - 1.39x=−1.39 D) x=3.49x = 3.49x=3.49 E) x=−0.69x = - 0.69x=−0.69

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Learning Objectives

Learning Objectives

Related questions

Solve the exponential equation. Round your answer to two decimal places. $7 ^ { x + 3 } - 5 = 18$

A) x= -0.77
B) $x = - 1.64$
C) $x = - 1.39$
D) $x = 3.49$
E) $x = - 0.69$