What is the answer to 14^{6x}=64^{x+3} ?

The answer to 14^{6x}=64^{x+3} is x=(3ln(2))/(ln(7))

Solve for x: 14^{6x}=64^{x+3}

The solution is x=(3ln(2))/(ln(7))

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1 4^{6 x} = 6 4^{x + 3}

x = \frac{3 ln ( 2 )}{ln ( 7 )}

Decimal

x = 1.06862 \dots

Solution steps

1 4^{6 x} = 6 4^{x + 3}

Apply exponent rules

6 x ln (14) = (x + 3) ln (64)

Solve

6 x ln (14) = (x + 3) ln (64) : x = \frac{3 ln ( 2 )}{ln ( 7 )}

x = \frac{3 ln ( 2 )}{ln ( 7 )}

[(4)^{2}]^{x} = 256

4^{- 2 x} \times 4^{x} = 64

6^{2 x} + 6^{x} - 56 = 0

5^{2 x - 1} + 2 = 7

e^{x} = 2

What is the answer to 14^{6x}=64^{x+3} ?
The answer to 14^{6x}=64^{x+3} is x=(3ln(2))/(ln(7))
Solve for x: 14^{6x}=64^{x+3}
The solution is x=(3ln(2))/(ln(7))