2⁵.8=2⁵.2³=2⁵⁺³=2⁸

3⁷/9=3⁷:3²=3^7–2=3⁵

2⁵x8=2⁵x2³=2⁸

3⁷:9=3⁷:3³=3⁴

\(2^n:8=512\)

=> \(2^n=512\cdot8\)

=> \(2^n=4096\)

=> \(2^n=2^{12}\)

=> n = 12

\(2^n\div8=512\)

\(\Rightarrow\)\(2^n=512\times8\)

\(\Rightarrow\)\(2^n=4096\)

\(\Rightarrow\)\(2^n=2^{12}\)

\(\Rightarrow\)\(n=12\)

8.2²¹

=2³.2²¹

=2²⁴

cách 2 nữa

1,

\(A=2^0+2^1+2^2+..+2^{2006}\)

\(=1+2+2^2+...+2^{2016}\)

\(2A=2+2^2+2^3+..+2^{2007}\)

\(2A-A=\left(2+2^2+2^3+..+2^{2007}\right)-\left(1+2+2^2+..+2^{2006}\right)\)

           \(A=2^{2017}-1\)

\(B=1+3+3^2+..+3^{100}\)

\(3B=3+3^2+3^3+..+3^{101}\)

\(3B-B=\left(3+3^2+..+3^{101}\right)-\left(1+3+..+3^{100}\right)\)

\(2B=3^{101}-1\)

\(\Rightarrow B=\frac{3^{100}-1}{2}\)

\(D=1+5+5^2+...+5^{2000}\)

\(5D=5+5^2+5^3+...+5^{2001}\)

\(5D-D=\left(5+5^2+..+5^{2001}\right)-\left(1+5+...+5^{2000}\right)\)

\(4D=5^{2001}-1\)

\(D=\frac{5^{2001}-1}{4}\)

các bn giúp mk nha càng nhanh càng tốt

ai nhanh mk TC cho

Xin lỗi bn , mk còn thiếu 1 câu :

\(8^{14}=4^N\)

\(\Rightarrow N=14.2\)

\(\Rightarrow N=28\)

a,\(8:2^N=2\)

\(2^N=8:2\)

\(2^N=4\)

\(2^N=2^2\)

b, \(8^n:2^n=4\)

\(\Rightarrow n=1\)

\(7x-140=147\)

\(7x=287\)

\(x=41\)

\(4.\left(x-3\right)=48\)

\(x-3=12\)

\(x=15\)

Lời giải:

\(2^{27}.3^{18}=(2^3)^9.(3^2)^9=8^9.9^9=(8.9)^9=72^9\)

\(25^4.2^8=25^4.(2^2)^4=25^4.4^4=(25.4)^4=100^4\)

\((-9)^4.27^2=9^4.27^2=(3^2)^4.(3^3)^2=3^8.3^6=3^{8+6}=3^{14}\)

\(-5^4:25=-5^4:(5^2)=-5^{4-2}=-5^2\)

Câu 1:

2.3^x = 10.3¹² + 8.27⁴

3^x = 9565938 : 2

3^x = 4782969

3^x = 3¹⁴

x = 14

Câu 2:

18 = 2.3²

\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{n\left(n+1\right)}=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{n\left(n+1\right)}\)

\(=\frac{2}{2\cdot3}+\frac{2}{3\cdot4}+\frac{2}{4\cdot5}+...+\frac{2}{n\left(n+1\right)}=1-\frac{2}{3}+\frac{2}{3}-\frac{2}{4}+\frac{2}{4}-\frac{2}{5}+...+\frac{2}{n}-\frac{2}{n+1}\)

Tới đây dễ rồi bạn rút gọn rồi tìm n