Đáp án:
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`1,`
`5^x + 5^{x+1}=150`
`-> 5^x + 5^x × 5 =150`
`-> 5^x × (1+5)=150`
`->5^x × 6=150`
`->5^x=150÷6`
`-> 5^x=25`
`->5^x=5^2`
`->x=2`
Vậy `x=2`
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`2,`
`(2x-1/4)^2=49/25`
`-> (2x-1/4)^2=(7/5)^2` hoặc `(2x-1/4)^2= ( (-7)/5)^2`
`->2x-1/4=7/5` hoặc `2x-1/4=(-7)/5`
`->2x=7/5+1/4` hoặc `2x=(-7)/5+1/4`
`->2x=33/20` hoặc `2x=(-23)/20`
`-> x=33/20 ÷2` hoặc `x=(-23)/20 ÷2`
`->x=33/40` hoặc `x=(-23)/40`
Vậy `x=33/40` hoặc `x=(-23)/40`
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`3,`
`(2x+1/2)^2=1/4`
`-> (2x+1/2)^2=(1/2)^2` hoặc `(2x+1/2)^2=( (-1)/2)^2`
`->2x+1/2=1/2` hoặc `2x+1/2=(-1)/2`
`->2x=1/2-1/2` hoặc `2x=(-1)/2-1/2`
`->2x=0` hoặc `2x=-1`
`->x=0÷2` hoặc `x=-1÷2`
`->x=0` hoặc `x=(-1)/2`
Vậy `x=0` hoặc `x=(-1)/2`
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`4,`
`33^{2x} ÷ 11^{2x}=81`
`-> (33÷11)^{2x}=81`
`-> 3^{2x}=81`
`-> 3^{2x}=3^4`
`->2x=4`
`->x=4÷2`
`->x=2`
Vậy `x=2`
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`5,`
`(2/3 +x)^3=27`
`-> (2/3+x)^3=3^3`
`->2/3+x=3`
`->x=3-2/3`
`->x=7/3`
Vậy `x=7/3`
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`6,`
`(2x-1/3)^2=( (-1)/6)^2`
`-> (2x-1/3)^2=1/36`
`-> (2x-1/3)^2=(1/6)^2` hoặc `(2x-1/3)^2=( (-1)/6)^2`
`->2x-1/3=1/6` hoặc `2x-1/3=(-1)/6`
`->2x=1/6+1/3` hoặc `2x=(-1)/6+1/3`
`->2x=1/2` hoặc `2x=1/6`
`->x=1/2÷2` hoặc `x=1/6÷2`
`->x=1/4` hoặc `x=1/12`
Vậy `x=1/4` hoặc `x=1/12`
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`7,`
`3^{x-1} + 5×3^{x-1}=162`
`-> 3^{x-1}×(1+5)=162`
`-> 3^{x-1}×6=162`
`-> 3^{x-1}=162÷ 6`
`->3^{x-1}=27`
`->3^{x-1}=3^3`
`->x-1=3`
`->x=3+1`
`->x=4`
Vậy `x=4`
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`8,`
`(2/3)^x=16/81`
`-> (2/3)^x=(2/3)^4`
`->x=4`
Vậy `x=4`
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`9,`
`(x + 2/3)^3=(-8)/27`
`-> (x+2/3)^3= ( (-2)/3)^3`
`->x+2/3=(-2)/3`
`->x=(-2)/3-2/3`
`->x=(-4)/3`
Vậy `x=(-4)/3`
