What is the answer to 5^t+3(5^{t-1})=400 ?

The answer to 5^t+3(5^{t-1})=400 is t=(ln(50))/(ln(5))+1

Solve for t: 5^t+3(5^{t-1})=400

The solution is t=(ln(50))/(ln(5))+1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

5^{t} + 3 (5^{t - 1}) = 400

t = \frac{ln ( 50 )}{ln ( 5 )} + 1

Decimal Notation

t = 3.43067 \dots

Solution steps

5^{t} + 3 (5^{t - 1}) = 400

Factor

5^{t} + 3 \cdot 5^{t - 1} : 8 \cdot 5^{t - 1}

8 \cdot 5^{t - 1} = 400

Divide both sides by

8

5^{t - 1} = 50

Apply exponent rules

(t - 1) ln (5) = ln (50)

Solve

(t - 1) ln (5) = ln (50) : t = \frac{ln ( 50 )}{ln ( 5 )} + 1

t = \frac{ln ( 50 )}{ln ( 5 )} + 1

ln (1 + e^{- 3 x}) = 2

4^{x} = 15

7^{x - 10} + 7^{x - 9} + 7^{x - 8} = 57

3^{y^{2} - 3 y} = 81

5^{x} + 5^{- x} = 6

What is the answer to 5^t+3(5^{t-1})=400 ?
The answer to 5^t+3(5^{t-1})=400 is t=(ln(50))/(ln(5))+1
Solve for t: 5^t+3(5^{t-1})=400
The solution is t=(ln(50))/(ln(5))+1