Question

X81** *34*=24681x + 1 + 3{4x } = 246" alt="81x + 1 + 3{4x } = 246" align="absmiddle" class="latex-formula">
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Answer 1

Answer:

$x=\frac{1}{4}$

Step-by-step explanation:

$81^{x+1}+3^{4x}=246$

$81=3^4$

Rewrite equation: $3^{4\left(x+1\right)}+3^{4x}=246$

$3^{4\left(x+1\right)}=3^{4x}\times 3^4$

$3^{4x}\times 3^4+3^{4x}=246$

Factor out $3^{4x}$:

$3^{4x}\left(3^4+1\right)=246$

Divide both sides by $(3^4+1)$:

$\frac{3^{4x}\left(3^4+1\right)}{3^4+1}=\frac{246}{3^4+1}$

$3^{4x}=\frac{246}{3^4+1}$

$3^{4x}=\frac{246}{82}$

$3^{4x}=3$

Anything to the power of 1 is itself. Hence,

$4x=1$

$x=\frac{1}{4}$