What is the answer to log_{3}(log_{10}(9x)+12+9^x)=2x ?

The answer to log_{3}(log_{10}(9x)+12+9^x)=2x is No Solution for x\in\mathbb{R}

Solve for x: log_{3}(log_{10}(9x)+12+9^x)=2x

The solution is No Solution for x\in\mathbb{R}

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lo g_{3} (lo g_{10} (9 x) + 12 + 9^{x}) = 2 x

No Solution for x \in R

Solution steps

lo g_{3} (lo g_{10} (9 x) + 12 + 9^{x}) = 2 x

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

3^{l o g_{3} (l o g_{10} (9 x) + 12 + 9^{x})} = 3^{2 x}

Simplify

3^{l o g_{3} (l o g_{10} (9 x) + 12 + 9^{x})} : lo g_{10} (9 x) + 12 + 9^{x}

Simplify

3^{2 x} : 9^{x}

lo g_{10} (9 x) + 12 + 9^{x} = 9^{x}

Subtract

9^{x}

from both sides

lo g_{10} (9 x) + 12 + 9^{x} - 9^{x} = 9^{x} - 9^{x}

Simplify

lo g_{10} (9 x) + 12 = 0

Move

12

to the right side

lo g_{10} (9 x) = - 12

Apply log rules

9 x = \frac{1}{1 0 ^{12}}

Solve

9 x = \frac{1}{1 0 ^{12}} : x = \frac{1}{1 0 ^{12} \cdot 9}

x = \frac{1}{1 0 ^{12} \cdot 9}

Verify Solutions:

x = \frac{1}{1 0 ^{12} \cdot 9}

False

The solution is

No Solution for x \in R

ln (x - 1) = 4.4

lo g_{10} (3 x + 1) = 1

0.26 = lo g_{10} (x)

lo g_{2} (x - 2) + lo g_{2} (x - 3) = 1

lo g_{10} (10 a) = 4

What is the answer to log_{3}(log_{10}(9x)+12+9^x)=2x ?
The answer to log_{3}(log_{10}(9x)+12+9^x)=2x is No Solution for x\in\mathbb{R}
Solve for x: log_{3}(log_{10}(9x)+12+9^x)=2x
The solution is No Solution for x\in\mathbb{R}