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Agata [3.3K]
3 years ago
10

NEED HELP What is the real value of x in the equation log.2.24 - log.2.3 = log.5.x ?

Mathematics
2 answers:
tia_tia [17]3 years ago
8 0

Answer:

125

Step-by-step explanation:

log2 (24) - log2 (3) = log5 (x)

We know that log a(b) - log a(c) = log a( b/c)

log2 (24/3)  = log5 (x)

log2 (8) = log5 (x)

Rewriting 8 as 2^3

log2 (2^3) = log5 (x)

We know that log a ( a^b) =  b loga (a) and loga (a) =1

3 log2 (2) = log5 (x)

3 *1 =  log5 (x)

3 = log5 (x)

We know log a (b) =c  can be written as a^c =b

5^3 = x

125 =x

sergey [27]3 years ago
6 0

Answer:

x = 125

Step-by-step explanation:

log2(24) - log2(3) = log5(x)

log2(8×3) - log2(3) = log5(x)

log2(8) + log2(3) - log2(3) = log5(x)

log(8) = log5(x)

log2(2³) = log5(x)

3log2(2) = log5(x)

3 = log5(x)

x = 5³

x = 125

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