What is the answer to 16=17^{t-2}+11 ?

The answer to 16=17^{t-2}+11 is t=(ln(5))/(ln(17))+2

Solve for t: 16=17^{t-2}+11

The solution is t=(ln(5))/(ln(17))+2

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16 = 1 7^{t - 2} + 11

t = \frac{ln ( 5 )}{ln ( 17 )} + 2

Decimal Notation

t = 2.56806 \dots

Solution steps

16 = 1 7^{t - 2} + 11

Switch sides

1 7^{t - 2} + 11 = 16

Move

11

to the right side

1 7^{t - 2} = 5

Apply exponent rules

(t - 2) ln (17) = ln (5)

Solve

(t - 2) ln (17) = ln (5) : t = \frac{ln ( 5 )}{ln ( 17 )} + 2

t = \frac{ln ( 5 )}{ln ( 17 )} + 2

2^{x} = 37

2^{x} = 28

2 5^{x + 1} + 3 \cdot 5^{x + 2} - 16 = 0

2. 5^{- 4 x} = 6.4

15 = 3 (8)^{- x - 4}

What is the answer to 16=17^{t-2}+11 ?
The answer to 16=17^{t-2}+11 is t=(ln(5))/(ln(17))+2
Solve for t: 16=17^{t-2}+11
The solution is t=(ln(5))/(ln(17))+2