Name: Logarithmic Inequalities
Uploaded: 2019-07-19
Duration: 10 min 24 s
Description: Logarithmic inequalities are inequalities in which one (or both) sides involve a logarithm. Watch this video and learn how to solve logarithmic inequalities.

Question

Find the values of

‘ b ’

for which the equation

2 \log_{\frac{1}{25}} (b x + 28) = - \log_{5} (12 - 4 x - x^{2})

has only one solution.

Accepted Answer

Given logarithmic equation is

$2 \log_{\frac{1}{25}} (b x + 28) = - \log_{5} (12 - 4 x - x^{2})$

$\Rightarrow 2 \log_{5^{2}} (b x + 28) = \log_{5} (12 - 4 x - x^{2})$

$\Rightarrow \frac{2}{2} \log_{5} (b x + 28) = \log_{5} (12 - 4 x - x^{2})$

$\Rightarrow b x + 28 = 12 - 4 x - x^{2}$

$\Rightarrow x^{2} + (b + 4) x + 16 = 0$

$∵$ The equation has only one solution

$∴$ Discriminant $D = 0$

$\Rightarrow {(b + 4)}^{2} - 4 \times 1 \times 16 = 0$

$\Rightarrow b^{2} + 8 b + 16 - 64 = 0$

$\Rightarrow b^{2} + 8 b - 48 = 0$

$\Rightarrow b^{2} + 12 b - 4 b - 48 = 0$

$\Rightarrow (b + 12) (b - 4) = 0$

$∴ b = - 12, b = 4$

Find the values of $‘ b ’$ for which the equation $2 \log_{\frac{1}{25}} (b x + 28) = - \log_{5} (12 - 4 x - x^{2})$ has only one solution.

Important Questions on Logarithm and Its Applications

Learn and Prepare for any exam you want !

Find the values of ‘b’ for which the equation 2log125bx+28=-log512-4x-x2 has only one solution.

Important Questions on Logarithm and Its Applications

Learn and Prepare for any exam you want !

Find the values of $‘ b ’$ for which the equation $2 \log_{\frac{1}{25}} (b x + 28) = - \log_{5} (12 - 4 x - x^{2})$ has only one solution.