[tex]\textrm{a)}\\ \\ 4^{2x+3} = 128^2\\ \\ {(2^2)}^{2x+3} = {(2^7)}^2 \\ \\ 2^{4x+6} = 2^14 \\ \\ 4x+6 = 14 \\ \\ 4x = 8\\ \\ x = 2[/tex]
[tex]\textrm{b)} \\ \\ 32^x = 8^{40}\\ \\ {(2^5)}^x = {2^3}^{40}\\ \\ 2^{5x} = 2^{120}\\ \\ 5x = 120\\ \\ x = 24[/tex]
[tex]\textrm{c)} \\ \\ 8^{2x+3} = 512^7\\ \\ {(2^3)}^{2x+3} = {(2^9)}^7\\ \\ 2^{6x+9} = 2^{63}\\ \\ 6x+9 = 63\\ \\ 6x = 54\\ \\ x = 9[/tex]
[tex]\textrm{d)} \\ \\ 27^{2x}\cdot 9^x = 81^6\\ \\ {(3^3)}^{2x} \cdot {(3^2)}^x = {(3^4)}^6\\ \\ 3^{6x} \cdot 3^{2x} = 3^{24}\\ \\ 3^{8x} = 3^{24}\\ \\ 8x = 24\\ \\ x = 3[/tex]
[tex]\textrm{e)} 9^{x+5} = 9^{3x}\cdot {(3^3)}^2\\ \\ {(3^2)}^{x+5} = {(3^2)}^{3x} \cdot 3^6\\ \\ 3^{2x+10} = 3^{6x+6}\\ \\ 2x + 10 = 6x + 6\\ \\ 4x = 4\\ \\ x = 1[/tex]
[tex]\textrm{f)} \\ \\ 8^x\cdot 4^x = 32^6\\ \\ {(2^3)}^x\cdot {(2^2)}^x = {(2^5)}^6 \\ \\ 2^{3x} \cdot 2^{2x} = 2^30\\ \\ 2^{5x} = 2^{30}\\ \\ 5x = 30\\ \\ x = 6[/tex]
[tex]\textrm{g)} \\ \\ 3^x \cdot 9^x\cdot 27^x = 81^3\\ \\ 3^x \cdot {(3^2)}^x\cdot {(3^3)}^x = {(3^4)}^3 \\ \\ 3^x\cdot 3^{2x}\cdot 3^{3x} = 3^{12}\\ \\ 3^{6x} = 3^{12} \\ \\ 6x = 12\\ \\ x = 2[/tex]
