Logarithm Basic(3)

Algebra Level 1

Solve for x in the equation

log ⁡ 4 ( x ) − log ⁡ 4 ( x − 1 ) = 1 2 . \log_4 (x) - \log_4 (x-1) = \frac{1}{2} .


The answer is 2.

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Mardokay Mosazghi by Mardokay Mosazghi , 22, USA

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2 solutions

Abhishek Singh
Jun 8, 2014

log ⁡ 4 ( x ) − log ⁡ 4 ( x − 1 ) = 1 2 \log_{4} {(x)}-\log_{4} {(x-1)}=\frac{1}{2} can be written as log ⁡ 4 x x − 1 = 1 2 \log _{4} {\frac{x}{x-1}}=\frac{1}{2} which means 4 1 2 = x x − 1 4^{\frac{1}{2}}=\frac{x}{x-1} hence x = 2 x=\boxed{2}

14 Helpful 0 Interesting 0 Brilliant 0 Confused

please can you give me a clear image of what a log is

Palash Som - 7 years ago

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Actually log ⁡ x y \log_{x}{y} means that what power of x x gives y y ? i.e. x ? = y 1 x^{?}=y^{1}

Abhishek Singh - 7 years ago

Logarithms are the "opposite" of exponentials, just as subtraction is the opposite of addition and division is the opposite of multiplication. Logs "undo" exponentials. Technically speaking, logs are the inverses of exponentials.

Mardokay Mosazghi - 7 years ago

got it thanks

Sandhya Naresh - 6 years, 11 months ago

you just have to transform it into exponential form

Sheila Palagtiw - 6 years, 10 months ago

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not necessarily

Subham Gupta - 6 years, 10 months ago
Rajkumar Seth
Aug 3, 2015

log(x/x-1) =(1/2)log2^2 x=2x-2 x=2

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Why cant we take sqrt 4 as +2 n -2 both here?

Manisha Bhosley - 5 years, 7 months ago

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