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Find the value of x if 4logx + 5logx - 7logx = 2log16

July 13, 2026Mathematics

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Answer

4

4 steps

Combine the terms involving $\log x$ on the left side of the equation.
$4\log x + 5\log x - 7\log x = \log 16$ $(4+5-7)\log x = \log 16$ $2\log x = \log 16$
Use the logarithm property $a\log b = \log(b^a)$ to rewrite the left side.
$\log(x^2) = \log 16$
Since $\log A = \log B$ implies $A=B$ , equate the arguments of the logarithms.
$x^2 = 16$
Solve for $x$ by taking the square root of both sides.
$x = \pm\sqrt{16}$ $x = \pm 4$
Since the argument of a logarithm must be positive, $x$ must be greater than 0. Therefore, we take the positive root.
$x = 4$
The value of $x$ is $\boxed{4}$ .

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