What is the answer to 4*9^{2x}+144^x-3*16^{2x}=0 ?

The answer to 4*9^{2x}+144^x-3*16^{2x}=0 is x=(527ln(4/3))/(276ln(3))

Solve for x: 4*9^{2x}+144^x-3*16^{2x}=0

The solution is x=(527ln(4/3))/(276ln(3))

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4 \cdot 9^{2 x} + 14 4^{x} - 3 \cdot 1 6^{2 x} = 0

x = \frac{527 ln ( \frac{4}{3} )}{276 ln ( 3 )}

Decimal Notation

x = 0.49999 \dots

Solution steps

4 \cdot 9^{2 x} + 14 4^{x} - 3 \cdot 1 6^{2 x} = 0

Divide both sides by

9^{2 x}

\frac{4 \cdot 9 ^{2 x}}{9 ^{2 x}} + \frac{14 4 ^{x}}{9 ^{2 x}} - \frac{3 \cdot 1 6 ^{2 x}}{9 ^{2 x}} = \frac{0}{9 ^{2 x}}

Simplify

4 + (\frac{16}{9})^{x} - \frac{3 \cdot 25 6 ^{x}}{8 1 ^{x}} = 0

Apply exponent rules

4 + (8 1^{x})^{0.13092 \dots} - \frac{3 ( 8 1 ^{x} ) ^{1.26185 \dots}}{8 1 ^{x}} = 0

Rewrite the equation with

8 1^{x} = u

4 + (u)^{0.13092 \dots} - \frac{3 ( u ) ^{1.26185 \dots}}{u} = 0

Solve

4 + u^{0.13092 \dots} - \frac{3 u ^{1.26185 \dots}}{u} = 0 : u = (\frac{4}{3})^{\frac{527}{69}}

u = (\frac{4}{3})^{\frac{527}{69}}

Substitute back

u = 8 1^{x},

solve for

x

Solve

8 1^{x} = (\frac{4}{3})^{\frac{527}{69}} : x = \frac{527 ln ( \frac{4}{3} )}{276 ln ( 3 )}

x = \frac{527 ln ( \frac{4}{3} )}{276 ln ( 3 )}

lo g_{10} (1 0^{x}) = 4

2^{2 x + 5} = 3^{x + 3}

7^{4} x + 1 = 5^{x}

2 = 2^{x}

4^{x} + 1 = 64

What is the answer to 4*9^{2x}+144^x-3*16^{2x}=0 ?
The answer to 4*9^{2x}+144^x-3*16^{2x}=0 is x=(527ln(4/3))/(276ln(3))
Solve for x: 4*9^{2x}+144^x-3*16^{2x}=0
The solution is x=(527ln(4/3))/(276ln(3))