The value of x for log (7 x+1)=log (x-2)+1 is 7.
Due of their connection to exponential functions, logarithmic functions are crucial. Exponential equations and the characteristics of exponential functions may both be investigated using logarithms. Additionally, they will be of great service in calculus, where they will be used to determine the slope of specific functions and the region enclosed by particular curves. They also have useful uses in economics.
Given,
log (7 x+1)=log (x-2)+1
log(7x + 1) - log(x - 2) = 1
using log (m/n) = log m - log n
log (7x+1 / x-2) = 1
It can be expressed as -
7x + 1 / x - 2 = 10 ¹
7x + 1 = 10x - 20
3x = 21
x = 7
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