Solve: 1/4 × log₆(1296) × log₆(1/2) - log₆(3) Expression

Question

14log61296log612log63= \frac{1}{4}\cdot\log_61296\cdot\log_6\frac{1}{2}-\log_63=

Video Solution

Solution Steps

00:00 Solve
00:25 Let's calculate the first logarithm
00:46 This is the solution to the logarithm
01:01 Let's substitute and reduce
01:20 We'll use the formula for subtracting logarithms
01:26 Subtracting logarithms equals the logarithm of the quotient
01:30 Let's use this formula in our exercise
01:53 We'll convert from number to fraction and calculate
01:59 Let's solve the logarithm
02:21 And this is the solution to the question

Step-by-Step Solution

We break it down into parts

log61296=x \log_61296=x

6x=1296 6^x=1296

x=4 x=4

144log612log63= \frac{1}{4}\cdot4\cdot\log_6\frac{1}{2}-\log_63=

log612log63= \log_6\frac{1}{2}-\log_63=

log6(12:3)=log616 \log_6\left(\frac{1}{2}:3\right)=\log_6\frac{1}{6}

log616=x \log_6\frac{1}{6}=x

6x=16 6^x=\frac{1}{6}

x=1 x=-1

Answer

1 -1


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