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# Solve the exponential equation $2\cdot 5^{\left(x-4\right)}+15=265$

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##  Final answer to the problem

$x=\log_{5}\left(78125\right)$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Solve for x
• Find the derivative using the definition
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1

Apply the property of the product of two powers of the same base in reverse: $a^{m+n}=a^m\cdot a^n$

$2\cdot 5^{-4}\cdot 5^x+15=265$

Learn how to solve logarithmic differentiation problems step by step online.

$2\cdot 5^{-4}\cdot 5^x+15=265$

Learn how to solve logarithmic differentiation problems step by step online. Solve the exponential equation 25^(x-4)+15=265. Apply the property of the product of two powers of the same base in reverse: a^{m+n}=a^m\cdot a^n. Calculate the power 5^{-4}. Multiply 2 times \frac{1}{625}. We need to isolate the dependent variable x, we can do that by simultaneously subtracting 15 from both sides of the equation.

##  Final answer to the problem

$x=\log_{5}\left(78125\right)$

##  Exact Numeric Answer

$x=7$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

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5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
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

###  Main Topic: Logarithmic Differentiation

The logarithmic derivative of a function f(x) is defined by the formula f'(x)/f(x).

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