7^2x=2^(x+4)

(2^(x+4)/49)

$$49x=2^x\times2^4\\\\
49x=2^x\times16\\\\
\frac{49}{16}x=2^x\\\\$$

I don't know what to do now 

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OR maybe you meant

$$7^{2x}=2^{x+4}\\\\
49^x=2^x2^4\\\\
49^x=16\times 2^x\\\\
\frac{49^x}{2^x}=16\\\\
\left(\frac{49}{2}\right)^x=16\\\\
log\left(\frac{49}{2}\right)^x=log16\\\\
xlog\left(\frac{49}{2}\right)=log16\\\\
x=log16\div log\left(\frac{49}{2}\right)\\\\
x=0.86679 \mbox{ (correct to 5 decimal places)}$$

I think that is right but I would like someone else to check it.