Solved Examples on Value of Log 7
Now let’s see some solved examples based on Value of Log 7.
Example 1: Solve \(log(4x-3)-log(x-4) = log 5\)
Solution:The above equation can be written in the form of
\(log(\frac{4x-3}{x-4}) = log 5\)
\(\frac{4x-3}{x-4} = 5\)
\(4x-3 = 5x-20\)
\(x = 17\)
The x value of the above equation is 17
Example 2: Express \(3logx+8log y = log b\) in Logarithmic free form.
Solution:Given \(3logx+8log y = log b\)
\(Log x^3 + log y^8 = log b\)
\(log(x^3 y^8) = log b\)
\(x^3 y^8 = b\)
The above equation in logarithm free form is \(x^3 y^8 = b\)
Example 3: Find the value of \(x =\sqrt{{(8432)^2\times(0.1259)\over{(27.478)^5}}}\)
Solution:\(x =\sqrt{{(8432)^2\times(0.1259)\over{(27.478)^5}}}\)
Let’s take log on both sides.
\(logx = log[\sqrt{{(8432)^2\times(0.1259)\over{(27.478)^5}}}]\)
\(logx = log[{{(8432)^2\times(0.1259)\over{(27.478)^5}}}]^{1\over2}\)
\(logx = {1\over2}[log(8432)^2 + log(0.1259) – log(27.478)^5]\)
\(logx = {1\over2}[2log(8432) + log(0.1259) – 5log(27.478)]\)
\(logx = {1\over2}[2log(8432) + log(0.1259) – 5log(27.478)]\)
\(logx = {1\over2}[2(3.9259) + \bar{1}.1000 – 5(1.4391)]\)
\(logx = {1\over2}[(7.8518) + \bar{1}.1000 – 7.1955]\)
\(logx = {1\over2}[\bar{1}.7563]\)
\(logx = {1\over2}[\bar{2} + 1.7563]\)
\(logx = [\bar{1}.8782]\)
antilog(x) = \(antilog(\bar{1}.8782)\)
x = 0.7554
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