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Solve the exponential equation $7^{\left(2x+1\right)}=3^{\left(x+2\right)}$

Step-by-step Solution

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Solution

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Final answer to the problem

$x=\frac{\ln\left(\frac{9}{7}\right)}{\ln\left(49\right)-\ln\left(3\right)}$
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Step-by-step Solution

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Learn how to solve simplification of algebraic expressions problems step by step online. Solve the exponential equation 7^(2x+1)=3^(x+2). Apply natural logarithm to both sides of the equation. Solve the product \ln\left(7\right)\left(2x+1\right). Using the power rule of logarithms: n\log_b(a)=\log_b(a^n). Solve the product \ln\left(3\right)\left(x+2\right).

Final answer to the problem

$x=\frac{\ln\left(\frac{9}{7}\right)}{\ln\left(49\right)-\ln\left(3\right)}$

Exact Numeric Answer

$x=0.0899734$

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Function Plot

Plotting: $7^{\left(2x+1\right)}- 3^{\left(x+2\right)}$

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0
a
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f
g
m
n
u
v
w
x
y
z
.
(◻)
+
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×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

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Main Topic: Simplification of algebraic expressions

The simplification of algebraic expressions consists in rewriting a long and complex expression in an equivalent, but much simpler expression. This simplification can be accomplished through the combined use of arithmetic and algebra rules.

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