Compute m

$8^{m}=32$ $2^{3m}=2^{5}$ $3m=5$ $m=\boxed{5}$

Hmmm.... Am I the only one who figured that since 32>8, m>1. 5/3 was the only number which satisfied that condition...

M=Log 32/Log8 = 1.66666666667=5/3

We can write $8^{m}=32$ as:

$2^{3m}=2^{5}$

(Same base means the exponents are equal)

$3m=5$

$m=\frac{5}{3}$

Thus, the answer is: $\boxed{m=\frac{5}{3}}$

$8^x>8$ iff $x>1$ , which only leaves $5/3$ .

Solve using logarithm:

8^m = 32

Log 8^m = Log 32

(m)(Log8) = Log 32

m = Log 32 / Log 8

m = 1.66666666667 or 5/3

8^m=32 2^3m=2^5 cancel base (2) 3m=5 then divide both side by 3 to reamain m. m=5/3

Omg, it's soooo challenging

8^m = 32

=> mlog2(8) = log2 (32)

[Log2(8) = 3, and log 2(32) = 5. Subbing these values in:]

=> 3m = 5 ( Divide by 3)

m = 5/3

Taking log we get, log 32 to the base 8 is m M = 5÷3

You don't even need to understand logs or exponent rules for this.

If m=1, 8^m=8. If m=2, 8^m=64. Therefore, it must be true that: 1<m<2. 5/3 is the only value that satisfies this requirement.

(8 to the power m)=32. It can also be written as : (2 to the power 3m)=(2 to the power 5); 3m=5; m=5\3

8 = 2^3 32 = 2^5

8^m = (2^3)^m 8^m = 32

(2^3)^m = 2^5 3m = 5 m = 5/3

Given, 8^m =32 2^3m =2^5 3m =5 m =5/3

$8^{m} = 32$

$log_2 8^{m} = log_2 32$

$m \times log_2 8 = log_2 32$

$m = log_2 32 / log_2 8$

$m = 5/3$

8^m=32

2^3m=32

2^3m=2^5

3m=5

m=5/3

mln8 = ln 32

m = ln 32 / ln 8

m = 1.66666666667 or 5/3

8^m = 32

(2^3)^m = 2^5

2^3m = 2^5

3m = 5

m=5/3

2^3m=2^5. so, 3m=5. hence m=5/3

log 32/log 8 = m

8^m=32

=>(2^3)^m=2^5

=>2^3m=2^5

=>3m=5

=>m=5/3

8^m=(2^3)^5/3

5/3 is the correct answer

Make Bases same for both the numbers ( of Base 2) and there u r Simple maths :-) m= 5/3

2^3m=2^5 =>3m=5 =>m=5/3

8=2^3 and 32=2^5

so 32=2^(5/3*3)......too get 8

32=(2^3)^5/3

32=(8)^5/3

so ans is 5/3

taking log on both sides, m log 8 = log 32 => 3m log 2 = 5 log 2 => 3m = 5 => m = 5/3

given, 8^{m} = 32 we know that 8 = 2^{3} and 32 = 2^{5} so, 2^{3}^{m} = 2^5 then, 3m = 5 m = 5/3

8^m=32 8^m=2^5 2^3m=2^5 3m=5 m=5/3

Taking Ln for both sides; Ln(8^m) = Ln(32) m.Ln(8) = Ln(32) m = Ln(32) / Ln(8) = 5/3

Log base 8 of 32 is 1.66666666667, equals to 5/3.

8^m=(2^3)^m and 32=2^5 therefore: 2^5 = (2^3)^m= 2^3m (exponential power rule) 5=3m m=5/3. q.e.d