What is the answer to xln(2)+ln(5)=ln(4^x-6) ?

The answer to xln(2)+ln(5)=ln(4^x-6) is x=(ln(6))/(ln(2))

Solve for x: xln(2)+ln(5)=ln(4^x-6)

The solution is x=(ln(6))/(ln(2))

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x ln (2) + ln (5) = ln (4^{x} - 6)

x = \frac{ln ( 6 )}{ln ( 2 )}

Decimal Notation

x = 2.58496 \dots

Solution steps

x ln (2) + ln (5) = ln (4^{x} - 6)

f (x) = g (x),

then

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

e^{x l n (2) + l n (5)} = e^{l n (4^{x} - 6)}

Simplify

e^{x l n (2) + l n (5)} : 5 \cdot 2^{x}

Simplify

e^{l n (4^{x} - 6)} : 4^{x} - 6

5 \cdot 2^{x} = 4^{x} - 6

Solve

5 \cdot 2^{x} = 4^{x} - 6 : x = \frac{ln ( 6 )}{ln ( 2 )}

x = \frac{ln ( 6 )}{ln ( 2 )}

Verify Solutions:

x = \frac{ln ( 6 )}{ln ( 2 )}

True

The solution is

x = \frac{ln ( 6 )}{ln ( 2 )}

ln (x) - ln (8) = ln (x + 5) - ln (2)

ln (x) + ln (3) = ln (9)

lo g_{6} (3 - m) + lo g_{6} (- m - 2) = 2

lo g_{6} (3 x) = 2

lo g_{10} (z) = 2

What is the answer to xln(2)+ln(5)=ln(4^x-6) ?
The answer to xln(2)+ln(5)=ln(4^x-6) is x=(ln(6))/(ln(2))
Solve for x: xln(2)+ln(5)=ln(4^x-6)
The solution is x=(ln(6))/(ln(2))