If $4^{[l o g_{2} l o g_{3} (4 x + 1)]} - l o g_{3} (4 x + 1)^{6} + 8 = 0$ and x>4, find $l o g_{4} (x - 4)$ .

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

$4^{[l o g_{2} l o g_{3} (4 x + 1)]} - l o g_{3} (4 x + 1)^{6} + 8 = 0$
det $l o g_{3} (4 x + 1) = a$
$\Rightarrow 4^{l o g_{2} a} - 6 a + 8 = 0$
$= 2^{2 l o g_{2} a} - 6 a + 8 = 0$
$= a^{2} - 6 a + 8 = 0$
a=4
$∴ l o g_{3} (4 x + 1) = 4$
$4 x + 1 = 3^{4}$
4x+1=81
x=20
or a=2
$l o g_{3} (4 x + 1) = 2$
4x+1=9
Rejected x=x<4
$∴ l o g_{4} (x - 4) = l o g_{4} (20 - 4) = l o g_{4} 16$
=2

Suggest Corrections

Similar questions

x

{log}_{2} (x - 16) = {log}_{4} (x - 4)

{log}_{2} x + {log}_{4} x + {log}_{16} x = \frac{21}{4}

x

{log}_{2} x + {log}_{4} x + {log}_{16} x = \frac{21}{4}

x

\div

\div

\frac{(36 \times 4) - 8 \times 4}{4 + 8 \times 2 + 16 \div 1} = ?

l o g_{2} x + l o g_{2} (\sqrt{x}) + l o g_{2} (\sqrt[4]{x}) + l o g_{2} (\sqrt[8]{x}) + l o g_{2} (\sqrt[16]{x}) + . . . . . = 4

Join BYJU'S Learning Program