Giải bài 1 trang 54 Toán 11 tập 2 Cánh diều

a) $(0,3)^{x-3}=1$

$<=> (0,3)^{x-3}=(0,3)^{0}$

$<=> x-3=0$

$<=> x=3$

b) $5^{3x-2}=25$

$<=> 5^{3x-2}=5^{2}$

$<=> 3x-2=2$

$<=> 3x=4$

$<=> x=\frac{4}{3}$

c) $9^{x-2}=243^{x+1}$

$<=>3^{2(x-2)}=3^{5(x+1)}$

$<=> 2x-4=5x+5$

$<=> -3x=9$

$<=> x=-3$

d) $log_{\frac{1}{2}}(x+1)=-3$

ĐKXĐ: $x+1>0 => x>-1$

$<=> log_{\frac{1}{2}}(x+1)=log_{\frac{1}{2}}(8)$

$<=> x+1=8 $

$<=> x=7$

e) $log_{5}(3x-5)=log_{5}(2x+1)$

ĐKXĐ: $x>\frac{5}{3}$

$<=> 3x-5=2x+1$

$<=> x=6$

g) $log_{\frac{1}{7}}(x+9)=log_{\frac{1}{7}}(2x-1)$

ĐKXĐ: $x>\frac{1}{2}$

$<=> x+9=2x-1$

$<=> x=10$