Solve the following equation for $x$ :
$3. x^{l o g_{5} 2} + 2^{l o g_{5} x} = 64$

Open in App

Solution

$3 x^{l o g_{5} 2} + 2^{l o g_{5} x} = 64$
$\Rightarrow {3.2}^{l o g_{5} x} + 2^{l o g_{5} x} = 64$
$\Rightarrow {4.2}^{l o g_{5} x} = 64$
$\Rightarrow 2^{l o g_{5} x} = 16 = 2^{4}$
$\Rightarrow l o g_{5} x = 4$
$∴ x = 5^{4} = 625$ .
Ans: 625

Suggest Corrections

Similar questions

\frac{1}{2} log (5 x - 4) + log \sqrt{x + 1} = 2 + log 0.18

2 {log}_{5} x - {log}_{x} 125 < 1

3 x^{{log}_{5} 2} + 2^{{log}_{5} x} = 64

x

\frac{3}{2^{log x}} = \frac{1}{64}

(x - 1)^{3} = 64

Join BYJU'S Learning Program