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Ratling [72]
3 years ago
7

Logarithm

Mathematics
1 answer:
aev [14]3 years ago
7 0

Answer:

1) (1/3)log_7(10); 3) log_8(u) - log_8(v); 5) 3ln(x)

Step-by-step explanation:

1)

log_7(^3sqrt(10))

log_7(10^1/3)

log_a(x^b) = b * log_a(x); when x >= 0.

(1/3)log_7(10)

About 0.39443...

3)

log_8(u/v)

log_c(a/b) = log_c(a) - log_c(b)

log_8(u) - log_8(v)

5)

ln(x^3)

log_a(x^b) = b * log_a(x); when x >= 0.

3ln(x)

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S_{100}=\dfrac{(2)(1)+(100-1)(1.5)}{2}\cdot100=\dfrac{2+(99)(1.5)}{1}\cdot50\\\\=(2+148.5)\cdot50=150.5\cdot50=7,525\\\\\boxed{S_{100}=7,525}\\\\Answer:\\the\ common\ difference:\ d=1.5\\the\ fifth\ term:\ a_5=7\\the\ sum\ of\ first\ 100\ terms:\ S_{100}=7,525

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