Type a math problem or upload a photo, screenshot, handwritten question...
error msg
- Algebra
- Calculus
- Trigonometry
- Matrix
- Differential
- Integral
- Trigonometry
- Letters
Question
3\times 16^{x}\times 2\times 81^{x}=5\times 36^{x}
Solve the equation
x=\frac{\log_{6}{\left(5\right)}-1}{2}
Alternative Form
x\approx -0.050878
Evaluate
3\times 16^{x}\times 2\times 81^{x}=5\times 36^{x}
Multiply
More Steps
Evaluate
3\times 16^{x}\times 2\times 81^{x}
Transform the expression
3\times 2^{4x}\times 2\times 81^{x}
Transform the expression
3\times 2^{4x}\times 2\times 3^{4x}
Multiply the terms with the same base by adding their exponents
3^{1+4x}\times 2^{4x}\times 2
Multiply the terms with the same base by adding their exponents
3^{1+4x}\times 2^{4x+1}
Calculate
\left(3\times 2\right)^{4x+1}
Simplify
6^{4x+1}
6^{4x+1}=5\times 36^{x}
Take the logarithm of both sides
\log_{6}{\left(6^{4x+1}\right)}=\log_{6}{\left(5\times 36^{x}\right)}
Evaluate the logarithm
4x+1=\log_{6}{\left(5\right)}+2x
Move the expression to the left side
4x+1-2x=\log_{6}{\left(5\right)}
Move the expression to the right side
4x-2x=\log_{6}{\left(5\right)}-1
Add and subtract
More Steps
Evaluate
4x-2x
Collect like terms by calculating the sum or difference of their coefficients
\left(4-2\right)x
Subtract the numbers
2x
2x=\log_{6}{\left(5\right)}-1
Divide both sides
\frac{2x}{2}=\frac{\log_{6}{\left(5\right)}-1}{2}
Solution
x=\frac{\log_{6}{\left(5\right)}-1}{2}
Alternative Form
x\approx -0.050878
Show Solutions
Graph
