Question

Solve? 3^(4x-7)= 4^(2x+3)

Answer 1

Try taking the ln of each side, and use logarithmic properties to simplify for x?

Answer 2

x is around 7.30591

Answer 3

\[\frac{9^{2x}}{3^7}=4^{2x}4^3\]
\[\frac{9^{2x}}{4^{2x}}=3^74^3\]
\[(\frac{9}{4})^{2x}=3^74^3\]
\[x=\frac{1}{2} \log_{9/4} (3^7 4^3)\]

Answer 4

3^(4x-7)=4^(2x+3)

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
ln(3^(4x-7))=ln(4^(2x+3))

The left-hand side of the equation is equal to the exponent of the logarithm argument because the base of the logarithm equals the base of the argument.
4xln(3)-7ln(3)=ln(4^(2x+3))

The exponent of a factor inside a logarithm can be expanded to the front of the expression using the third law of logarithms. The third law of logarithms states that the logarithm of a power of x is equal to the exponent of that power times the logarithm of x (e.g. log^b(x^(n))=nlog^b(x)).
4xln(3)-7ln(3)=((2x+3)ln(4))

Multiply ln(4) by each term inside the parentheses.
4xln(3)-7ln(3)=(2xln(4)+3ln(4))

Since 2xln(4) contains the variable to solve for, move it to the left-hand side of the equation by subtracting 2xln(4) from both sides.
4xln(3)-7ln(3)-2xln(4)=3ln(4)

Factor out the GCF of 2x from each term in the polynomial.
2x(2ln(3))+2x(-ln(4))=7ln(3)+3ln(4)

Factor out the GCF of 2x from 4xln(3)-2xln(4).
2x(2ln(3)-ln(4))=7ln(3)+3ln(4)

Divide each term in the equation by (2ln(3)-ln(4)).
(2x(2ln(3)-ln(4)))/(2ln(3)-ln(4))=(7ln(3))/(2ln(3)-ln(4))+(3ln(4))/(2ln(3)-ln(4))

Simplify the left-hand side of the equation by canceling the common factors.
2x=(7ln(3))/(2ln(3)-ln(4))+(3ln(4))/(2ln(3)-ln(4))

Simplify the right-hand side of the equation by simplifying each term.
2x=(7ln(3)+3ln(4))/(2ln(3)-ln(4))

Divide each term in the equation by 2.
(2x)/(2)=(7ln(3)+3ln(4))/(2ln(3)-ln(4))/(2)

Simplify the left-hand side of the equation by canceling the common factors.
x=(7ln(3)+3ln(4))/(2ln(3)-ln(4))/(2)

Simplify the right-hand side of the equation by simplifying each term.
x=(7ln(3)+3ln(4))/(2(2ln(3)-ln(4)))

x=0.6166

Answer 5

take log both sides, think someone else asked this aswell:
log3^(4x-7)=log4^(2x+3)
4x-7/2x+3=log4/log3
4x-7/2x+3=1.26
(2x+3)(1.26)=4x-7
2.52x+3.78=4x-7
3.78+7=4x-2.52x
10.78=1.48x
10.78/1.48=x
7.28=x