\[\eqalign{ & a]\;3x + 5x = {7^2} - {3^2} \cr & [3 + 5]x = 49 - 9 \cr & 8x = 40 \cr & x = 40:8 \cr& x = 5 \cr & b]\;{3^x} = 27 \cr & {3^x} = {3^3} \cr& x = 3 \cr & c]\;{2^x}:{2^3} = 1 \cr & {2^{x - 3}} = {2^0} \cr & x - 3 = 0 \cr& x = 3 \cr & d]\;27 < {3^x} < 243 \cr & {3^3} < {3^x} < {3^5} \cr & 3 < x < 5 \cr& x = 4 \cr & e]\;{4^{x - 3}} = 16 \cr & {4^{x - 3}} = {4^2} \cr & x - 3 = 2 \cr & x = 2 + 3 \cr & x = 5 \cr} \]
Đề bài
Tìm số tự nhiên x, biết :
\[\eqalign{ & a]\;3x + 5x = {7^2} - {3^2} \cr & b]\;{3^x} = 27 \cr & c]\;{2^x}:{2^3} = 1 \cr & d]\;27 < {3^x} < 243 \cr & e]\;{4^{x - 3}} = 16. \cr} \]
Lời giải chi tiết
\[\eqalign{ & a]\;3x + 5x = {7^2} - {3^2} \cr & [3 + 5]x = 49 - 9 \cr & 8x = 40 \cr & x = 40:8 \cr& x = 5 \cr & b]\;{3^x} = 27 \cr & {3^x} = {3^3} \cr& x = 3 \cr & c]\;{2^x}:{2^3} = 1 \cr & {2^{x - 3}} = {2^0} \cr & x - 3 = 0 \cr& x = 3 \cr & d]\;27 < {3^x} < 243 \cr & {3^3} < {3^x} < {3^5} \cr & 3 < x < 5 \cr& x = 4 \cr & e]\;{4^{x - 3}} = 16 \cr & {4^{x - 3}} = {4^2} \cr & x - 3 = 2 \cr & x = 2 + 3 \cr & x = 5 \cr} \]