Question

Помогите решить логарифмические уравнения, с развёрнутым ответом

Answer 1

1.

$log_9x=2\|::log _a(b)=cquad Rightarrowquad b=a^c\|::log _9(x)=2quad Rightarrowquad x=9^2\x=9^2\x=81$

2.

$log_{frac{1}{4}} x=3\|::log _a(b)=cquad Rightarrowquad b=a^c\|::log _{frac{1}{4}}left(xright)=3quad Rightarrow quad :x=left(frac{1}{4}right)^3\x=left(frac{1}{4}right)^3\x=frac{1}{64}$

3.

$log_2left(3x-1right)=5\|::log _aleft(bright)=cquad Rightarrow quad b=a^c\|::log _2left(3x-1right)=5quad Rightarrow quad :3x-1=2^5\3x-1=2^5\3x=33\x=11$

4.

$log_5left(3-2xright)=2\|::log _aleft(bright)=cquad Rightarrow quad b=a^c\|::log _5left(3-2xright)=2quad Rightarrow quad :3-2x=5^2\3-2x=5^2\-2x=22\x=-11$

5.

$log_3left(frac{x}{4}-2 right)=1\|::log _aleft(bright)=cquad Rightarrow quad b=a^c\|::log _3left(frac{x}{4}-2right)=1quad Rightarrow quad frac{x}{4}-2=3^1\frac{x}{4}-2=3^1\frac{x}{4}cdot :4-2cdot :4=3^1cdot :4\x-8=12\x=20$

6.

$log_{frac{1}{2}}:left(4+6xright)=-4\|::log _aleft(bright)=cquad Rightarrow quad b=a^c\|::log _{frac{1}{2}}left(4+6xright)=-4quad Rightarrow quad :4+6x=left(frac{1}{2}right)^{-4}\4+6x=left(frac{1}{2}right)^{-4}\4+6x=16\6x=12\x=2$

7.

$log_{frac{1}{6}}:left(frac{x}{2}+10right)=-2\|::log _aleft(bright)=cquad Rightarrow quad b=a^c\|:: log _{frac{1}{6}}left(frac{x}{2}+10right)=-2quad Rightarrow quad frac{x}{2}+10=left(frac{1}{6}right)^{-2}\frac{x}{2}+10=left(frac{1}{6}right)^{-2}\frac{x}{2}cdot :2+10cdot :2=left(frac{1}{6}right)^{-2}cdot :2\x+20=72\x=52$

8.

$log_{frac{1}{3}}:left(6-5xright)=0\|::log _aleft(bright)=cquad Rightarrow quad b=a^c\|::log _{frac{1}{3}}left(6-5xright)=0quad Rightarrow quad :6-5x=left(frac{1}{3}right)^0 \6-5x=left(frac{1}{3}right)^0\6-5x=1\-5x=-5\x=1$