if $343^x = 49^{4-x}$, what is the value of $x$?

* $\frac{5}{8}$
* $\frac{8}{5}$
* 2
* 8

Question

if $343^x = 49^{4-x}$, what is the value of $x$?

* $\frac{5}{8}$
* $\frac{8}{5}$
* 2
* 8

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponential Equations" ], "new_concepts": [], "current_concepts": [ "Exponential Equations" ] } ## Express bases as powers of 7 $$ \begin{aligned} 343 &= 7^3 \ 49 &= 7^2 \end{aligned} $$ ## Substitute and apply exponent rules $$ \begin{aligned} (7^3)^x &= (7^2)^{4-x} \ 7^{3x} &= 7^{2(4-x)} \ 7^{3x} &= 7^{8-2x} \end{aligned} $$ ## Equate exponents and solve for x $$ \begin{aligned} 3x &= 8 - 2x \ 5x &= 8 \ x &= \frac{8}{5} \end{aligned} $$

(A) $\frac{5}{8}$

(B) $\frac{8}{5}$

(C) 2

(D) 8

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Exponential Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Express bases as powers of 7

Substitute and apply exponent rules

Equate exponents and solve for x

Answer: