LOGARITMOS

RESOLUCION DE ECUACIONES 3^X=8 X log 3 =log 8 X= log 8 /log 3 X= .9030/.4771 X=1.8863 5^(2x-1 )=2 (2x-1) log 5 =log 2 2x-1=log2/log5 2x-1= .3010/.6989 2x-1=.4306 2x=.4306+1 2x=1.4306 X=1.4306/2 X=.7153 EJERCICIOS 5^x=.17 X log 5 = log .17 X= log .17/ log 5 X= -0.7695/0.6989 X=-1.1010 〖.18〗^x=3.16 X log .18 = log 3.16 X=log 3.16/ log .18 X= 0.4996/ - 0.7447 X=- 0.6708 〖2.5〗^2x=4 (2x) log 2.5 = log 4 2x= log 4/ log 2.5 2x= 0.6020/ 0.3979 2x=1.5129 X=1.5129/2 X=0.75645 9^x=8 X log 9= log 8 X= log 8/ log 9 X= 0.9030/0.9542 X=0.9463 〖1.5〗^5x=5.5 (5x) log 1.5= log 5.5 5x= log 5.5/ log 1.5 5x= 0.7403/0.1760 5x= 4.2062 X=4.2062/5 X=0.84124 3^3x=9 (3x) log 3 = log 9 3x= log 9/ log 3 3x= 0.9542/ 0.4771 3x=2 X=2/3 X= 0.6666 3^(2x+5)=5 (2x+5) log 3 = log 5 2x+5 = log 5/ log 3 2x+5= 0.6989/ 0.4771 2x+5= 1.4648 2x=1.4648-5 2x=-3.5352 X= - 3.5352/2 X= - 1.7676 〖2.5〗^(2x-2)=10 (2x-2) log 2.5= log 10 2x-2= log 10/ log 2.5 2x-2= 1/0.3979 2x-2= 2.5131 2x= 2.5131+2 2x= 4.5131 X=4.5131/2 X= 2.25655 9^(5x-3)=6 (5x-3) log 9 = log 6 5x-3= log6 / log 9 5x-3 = 0.7781/0.9542 5x-3=0.8154 5x=0.8154+3 5x=3.8154 X= 3.8154/5 X= 0.7630 〖3.5〗^(3x-1)=2.5 (3x-1) log 3.5= log 2.5 3x-1= log 2.5/ log 3.5 3x-1= 0.3979/ 0.5440 3x-1= 0.7314 3x=0.7314+1 3x=1.7314 X=1.7314/3 X=0.5771 3^x=20 X log 3= log 20 X= log 20/ log 3 X= 1.3010/0.4771 X=2.7268 2^5x=.97 (5x) log 2= log .97 5x= log .97/log 2 5x= -0.0132/0.3010 5x=-0.0438 X= -0.0438/5 X=- 0.0087 〖3.5〗^(7x-1)= .87 (7x-1) log 3.5= log .87 7x-1 =log .87/ log 3.5 7x-1= - 0.0604/0.5440 7x-1= -0.1110 7x=-0.1110+1 7x=0.889 X=0.889/7 X=0.127 〖.97〗^2x=.56 (2x) log .97= log .56 2x=log⁡〖.56/log⁡〖.97〗 〗 2x= -0.2518/-0.0132 2x= 19.0757 X=10.0757/2 X=9.5378 2^3x=.89 (3x) log 2 = log .89 3x= log .89/ log 2 3x= -0.0506/0.3010 3x= -0.1681 X= -0.1681/3 X= -0.0560 5^3x=.58 (3x) log 5 = log .58 3x= log .58/ log 5 3x= -0.2365/0.6989 3x= -0.3383 X= -0.3383/3 X= -0.1127 〖2.3〗^(5x-1)=.9 (5x-1) log 2.3= log .9 5x-1= log .9/log 2.3 5x-1= -0.0457/0.3617 5x-1= -0.1152 5x=-0.1152+1 5x=0.8848 X=0.8848/5 X=0.1769 2^x=27 X log 2= log 27 X= log 27/log 2 X= 1.4313/0.3010 X=4.7551 3^2x=10.5 (2x) log 3= log 10.5 2x= log 10.5/ log 3 2x= 1.0211/0.4771 2x=2.1402 X=2.1402/2 X=1.0701 9^(7x-10)=1 (7x-10) log 9= log 1 7x-10= log 1/ log 9 7x-10= 0/0.9542 7x-10=0 7x=0+10 7x=10 X=10/7 X=1.4285 〖4.6〗^x=35 (x) log 4.6= log 35 X= log 35/ log 4.6 X= 1.5440/0.6627 X=2.3298 2^(.7x)=.7 (.7x) log 2 = log .7 .7x= log .7/log 2 .7x= -0.1549/0.3010 .7x= -0.5146 X=-0.5246/.7 X= - 0.7351 〖.2〗^2x=.5 (2x) log .2 = log .5 2x=log⁡〖.5〗 / log .2 2x= -0.3010/-0.6989 2x=0.4306 X=0.4306/2 X=0.2153 〖3.5〗^x=3.6 (x) log 3.5 = log 3.6 X= log 3.6/ log 3.5 X= 0.5563/0.5440 X=1.0226 2^(7x+1)=7 (7x+1) log 2 = log 7 7x+1= log 7 / log 2 7x+1= 0.8450/0.3010 7x+1= 2.8073 7x= 2.8073-1 7x= 1.8073 X= 1.8073/7 X= 0.2581 Resuelve las siguientes ecuaciones 7^(x+6)=5 (x+6) log 7= log 5 X+6= log 5/ log 7 X+6= 0.6989/0.8450 X+6= 0.8271 X=0.8271-6 X=- 5.1728 8^(2x-7)=3 (2x-7) log 8= log 3 2x-7 = log 3/ log 8 2x-7= 0.4771/ 0.9030 2x-7= 0.5283 2x= 0.5283+7 2x= 7.5283 X= 7.5283/ 2 X= 3.7641 4^(3x-5)=2 (3x-5) log 4= log 2 3x-5 = log 2/ log 4 3x-5= 0.3010/0.6020 3x-5= 0.5 3x=0.5+5 3x=5.5 X= 5.5/3 X= 1.8333 3^(1/2x-2)=.75 (1/2x-2) log 3= log .75 1/2x-2= log .75/ log 3 1/2x-2= -0.1249/0.4771 1/2x-2= -0.2617 1/2x= -0.2617+2 1/2x= 1.7382 X= 1.7382/ ½ X= 3.4764 9^(3/2x+1/2)=1.5 (3/2x+1/2) log 9= log 1.5 3/2x+1/2= log 1.5/log 9 3/2x+1/2= 0.1760/0.9542 3/2x+1/2= 0.1844 3/2x=0.1844-1/2 3/2x= -0.3155 X= -0.3155/3/2 X= - 0.2103 〖.25〗^(3/2x)=.5 (3/2x) log .25= log .5 3/2x=log⁡〖.5〗 / log .25 3/2x= -0.3010/-0.6020 3/2x=0.5 x=0.5/ 3/2 x=0.3333 〖3.6〗^1.7x=.8 (1.7x) log 3.6= log .8 1.7x= log .8/ log 3.6 1.7x= -0.0969/0.5563 1.7x= -0.1741 X= -0.1741/1.7 X= -0.1024 〖1.5〗^3x=2.5 (3x) log 1.5= log 2.5 3x= log 2.5/ log 1.5 3x= 0.3979/ 0.1760 3x= 2.2607 X= 2.2607/3 X= 0.7535 〖2.3〗^(5/2x)=5 (5/2x) log 2.3= log 5 5/2x= log 5/ log 2.3 5/2x= 0.6989/ 0.3617 5/2x= 1.9322 X= 1.9322/ 5/2 X= 0.77288 2^(7/3x)=4/5 (7/3x) log 2= log 4/5 7/3x= log 4/5 /log 2 7/3x= -0.0969/ 0.3010 7/3x= -0.3219 X= -0.3219/7/3 X= -0.1379 〖.8〗^x=2.2 (x) log. 8= log 2.2 X= log 2.2/ log .8 X= 0.3424/ -0.0969 X= -3.5335 〖.17〗^x= .7 (x) log .17= log .7 x= log.7/log.17 x= -0.1549/-0.7695 x=4.9677 〖3/2〗^x=3/2 (x) log 3/2= log 3/2 X= log 3/2/ log 3/2 X= 0.1760/0.1760 X= 1 〖.56〗^x= .97 (x) log .56= log .97 x= log .97/ log .56 x= -0.0132/ -0.2518 x= 0.0524 〖.8〗^x=2.3 (x) log .8= log 2.3 x= log 2.3/ log .8 x= 0.3617/-0.0969 x= -3.7327 4^(3x+7-2x)=36 (3x+7-2x) log 4 = log 36 3x+7-2x= log 36 / log 4 3x+7-2x= 1.5563/ 0.6020 3x+7-2x= 2.5852 3x-2x= 2.5852-7 3x-2x= -4.4148 X= -4.4148 3^(2/3x)=4 (2/3x) log 3= log 4 2/3x= log 4/ log 3 2/3x= 0.6020/ 0.4771 2/3x= 1.2617 X= 1.2617/ 2/3 X= 1.8926 2^(7x-3-2x+6)=10 (7x-3-2x+6) log 2 = log 10 7x-3-2x+6= log 10/ log 2 7x-3-2x+6= 1/ 0.3010 7x-3-2x+6= 3.3222 7x-2x= 3.3222-3+6 7x-2x= 0.3222 5x= 0.3222 X= 0.3222/5 X= 0.06444 〖5.7〗^(2/3x-7)=0.67 (2/3x-7) log 5.7= log 0.67 2/3x-7= log 0.67/ log 5.7 2/3x-7= -0.1739/0.7558 2/3x-7= -0.2300 2/3x= -0.2300+7 2/3x= 6.7699 X= 6.7699/2/3 X= 10.1548 〖2.3〗^(.5x-2)=.7 (.5x-2) log 2.3= log .7 .5x-2= log .7/ log 2.3 .5x-2= -0.1549/0.3617 .5x-2= -0.4282 .5x= -0.4282+2 .5x= 1.5717 X= 1.5717/.5 X= 3.1434 〖3.7〗^(2x-3+7x-1)=2 (2x-3+7x-1) log 3.7= log 2 2x-3+7x-1= log 2/ log 3.7 2x-3+7x-1= 0.3010/ 0.5682 2x-3+7x-1= 0.5297 2x+7x= 0.5297+3+1 2x+7x= 4.5297 9x= 4.5297 X= 4.5297/9 X= 0.5033 〖2.5〗^(1/2x)=.9 (1/2x) log 2.5= log .9 1/2x= log .9/ log 2.5 1/2x= -0.0457/0.3979 1/2x= -0.1148 X= -0.1148/ ½ X= -0.2297 〖3.2〗^(7x-3)=5 (7x-3) log 3.2= log 5 7x-3= log 5/ log 3.2 7x-3= 0.6989/ 0.5051 7x-3= 1.3836 7x= 1.3836+3 7x= 4.3836 X= 4.3836/7 X= 0.6262 4^(3x-7)=2.4 (3x-7) log 4= log 2.4 3x-7= log 2.4/ log 4 3x-7= 0.3882/ 0.6020 3x-7= 0.6315 3x= 0.6315+7 3x= 7.6315 X=7.6315/3 X= 2.5438 〖1.5〗^(6x-3)=4.7 (6x-3) log 1.5= log 4.7 6x-3= log 4.7/ log 1.5 6x-3= 0.6720/0.1760 6x-3= 3.8181 6x= 3.8181+3 6x= 6.8181 X= 6.8181/6 X= 1.1363