Solve the following exponential equations: 274x = 9^x+1 and ((1)/(8))^-2x = 2^x+3.

April 15, 2026Mathematics

ScanSolve AI Answer

April 15, 2026

Answer

$x = \frac{1}{5}$

Step 1: Solve $27^{4x} = 9^{x+1}$ . We express both sides with the same base, $3$ . $(3^3)^{4x} = (3^2)^{x+1}$ $3^{12x} = 3^{2(x+1)}$ Equate the exponents: $12x = 2x + 2$ $10x = 2$ $x = \frac{2}{10}$ $x = \frac{1}{5}$ The solution is $\boxed{x = \frac{1}{5}}$ .

Step 2: Solve $(\frac{1}{8})^{-2x} = 2^{x+3}$ . We express both sides with the same base, $2$ . $(2^{-3})^{-2x} = 2^{x+3}$ $2^{6x} = 2^{x+3}$ Equate the exponents: $6x = x + 3$ $5x = 3$

Was this helpful?

Need help with your own homework?

Get instant step-by-step solutions to any question. Free to start.

Ask Your Question

More Mathematics Questions

Qb) How many Spectators were there on Stands B and C all together? c) 458- d) what is double the numb…QThere were 1764 people at the soccer match on Sunday. a) Round this number off to the nearest 1000.…QIdentify these shapes. Write in your exercise book the name of the shape and the number of sides it…QThe quantities P, Q and R are such that P varies directly as Q and inversely as the square root of R…QIdentify the name, whether they have straight or curved sides, and if they are polygons, for the giv…

See all Mathematics questions →

Still have questions?

Quick Answer

Solve 27^4x = 9^x+1. We express both sides with the same base, 3.

Asked on April 15, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 15, 2026

Step 1: Solve 27^4x = 9^x+1. We express both sides with the same base, 3. (3^3)^4x = (3^2)^x+1 3^12x = 3^2(x+1) Equate the exponents: 12x = 2x + 2 10x = 2 x = (2)/(10) x = (1)/(5) The solution is x = (1)/(5). Step 2: Solve ((1)/(8))^-2x = 2^x+3. We express both sides with the same base, 2. (2^-3)^-2x = 2^x+3 2^6x = 2^x+3 Equate the exponents: 6x = x + 3 5x = 3