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# log question

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log 15 base 4 = x find x to 3 dp (with working please. thanks so much)

Guest Mar 22, 2017
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#1
+10800
+1

logbase4(15) = x

by definition of logs     15 = 4^x

take log base 10 of both sides

log 15 = log(4^x)

log 15 = x log 4

x = log 15/log 4  = 1.95344 ~ 1.953

ElectricPavlov  Mar 22, 2017
#2
+6925
0

Use base change formula.

$$\log_415 = x\\ x = \dfrac{\ln 15}{\ln 4} \approx 1.953$$

MaxWong  Mar 23, 2017

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