Đáp án:

Giải thích các bước giải:

$1.2^x=4^3$

$⇒2^x=2^6$

$⇒x=6$

$2.2^x=8^3$

$⇒2^x=2^9$

$⇒x=9$

$3.\left (\dfrac{1}{7} \right )^x=\left (\dfrac{1}{343} \right )^3$

$⇒\left (\dfrac{1}{7} \right )^x=\left (\dfrac{1}{7} \right )^9$

$⇒x=9$

$4.\left (\dfrac{6}{7} \right )^x=\left (\dfrac{213}{343} \right )^{111}$

$⇒\left (\dfrac{6}{7} \right )^x=\left (\dfrac{6}{7} \right )^{333}$

$⇒x=333$

$5.2^{5x+2}=8^9$

$⇒2^{5x+2}=2^{27}$

$⇒5x+2=27$

$⇒5x=25$

$⇒x=5$

$6.2^{7x+4}=32^{12}$

$⇒2^{7x+4}=2^{60}$

$⇒7x+4=60$

$⇒7x=56$

$⇒x=8$

$7.4^{-1-5x}=16^{12}$

$⇒4^{-1-5x}=4^24$

$⇒-1-5x=24$

$⇒-5x=25$

$⇒x=-5$

Đáp án:

\(1)\ x=6\\ 2)\ x=9\\ 3)\ x=9\\ 4)\ x=333\\ 5)\ x=5\\ 6)\ x=8\\ 7)\ x=(-5)\)

Giải thích các bước giải:

\(1)\ 2^x=4^3\\ ⇔2^x=(2^2)^3\\ ⇔2^x=2^6\\ ⇔x=6\\ \text{Vậy x = 6}\\ 2)\ 2^x=8^3\\ ⇔2^x=(2^3)^3\\ ⇔2^x=2^9\\ ⇔x=9\\ \text{Vậy x = 9}\\ 3)\ \bigg(\dfrac{1}{7}\bigg)^x=\bigg(\dfrac{1}{343}\bigg)^3\\ ⇔\bigg(\dfrac{1}{7}\bigg)^x=\bigg[\bigg(\dfrac{1}{7}\bigg)^3\bigg]^3\\ ⇔\bigg(\dfrac{1}{7}\bigg)^x=\bigg(\dfrac{1}{7}\bigg)^9\\ ⇔x=9\\ \text{Vậy x = 9}\\ 4)\ \bigg(\dfrac{6}{7}\bigg)^x=\bigg(\dfrac{216}{343}\bigg)^{111}\\ ⇔\bigg(\dfrac{6}{7}\bigg)^x=\bigg[\bigg(\dfrac{6}{7}\bigg)^3\bigg]^{111}\\ =\bigg(\dfrac{6}{7}\bigg)^x=\bigg(\dfrac{6}{7}\bigg)^{333}\\ ⇔x=333\\ \text{Vậy x = 333}\\ 5)\ 2^{5x+2}=8^9\\ ⇔2^{5x+2}=(2^3)^9\\ ⇔2^{5x+2}=2^{27}\\ ⇔5x+2=27\\ ⇔5x=25\\ ⇔x=5\\ \text{Vậy x = 5}\\ 6)\ 2^{7x+4}=32^{12}\\ ⇔2^{7x+4}=(2^5)^{12}\\ ⇔2^{7x+4}=2^{60}\\ ⇔7x+4=60\\ ⇔7x=56\\ ⇔x=8\\ \text{Vậy x = 8}\\ 7)\ 4^{-1-5x}=16^{12}\\ ⇔4^{-1-5x}=(4^2)^{12}\\ ⇔4^{-1-5x}=4^{24}\\ ⇔-1-5x=24\\ ⇔5x=-25\\ ⇔x=-5\\ \text{Vậy x = (- 5)}\)

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