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

14⋅log⁡61296⋅log⁡612−log⁡63= \frac{1}{4}\cdot\log_61296\cdot\log_6\frac{1}{2}-\log_63=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
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 written solution

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1

Understand the problem

14⋅log⁡61296⋅log⁡612−log⁡63= \frac{1}{4}\cdot\log_61296\cdot\log_6\frac{1}{2}-\log_63=

2

Step-by-step solution

We break it down into parts

log⁡61296=x \log_61296=x

6x=1296 6^x=1296

x=4 x=4

14⋅4⋅log⁡612−log⁡63= \frac{1}{4}\cdot4\cdot\log_6\frac{1}{2}-\log_63=

log⁡612−log⁡63= \log_6\frac{1}{2}-\log_63=

log⁡6(12:3)=log⁡616 \log_6\left(\frac{1}{2}:3\right)=\log_6\frac{1}{6}

log⁡616=x \log_6\frac{1}{6}=x

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

x=−1 x=-1

3

Final Answer

−1 -1

Practice Quiz

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\( \log_{10}3+\log_{10}4= \)

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